The words "slave" and "surrender" do not appear next to each other anywhere within the series.
However, there are quite a few quotes which describe or speak of a slave surrendering.
She did not move, and then suddenly I felt the cut of her nails deep in my arms, and though her lips were open, her teeth were clenched, her head was back, the eyes closed, her hair tangled under her and over her body, and then her eyes seemed surprised, startled, and her shoulders lifted a bit from the rug, and she looked at me, and I could feel the beginning in her, the breathing of it and the blood of it, hers, in my own flesh swift and like fire in her beauty, mine, and knowing it was then the time, meeting her eyes fiercely, I said to her, with sudden contempt and savagery, following the common Gorean Rites of Submission, "Slave!" and she looked at me with horror and cried out "No!" and half reared from the rug, wild, helpless, fierce as I intended, wanting to fight me, as I knew she would, wanting to slay me if it lay within her power, as I knew she would, and I permitted her to struggle and to bite and scratch and cry out and then I silenced her with the kiss of the master, and accepted the exquisite surrender which she had no choice but to give. "Slave," she wept. "slave, slave, slave - I am slave!"
Nomads of Gor    Book 4    Page 303
Passion, it is thought, deprives the free woman to some extent of her freedom and important self-control; it is frowned upon because it makes her behave, to some extent, like a degraded female slave; free women, thus, to protect their honor and dignity, their freedom and personhood, their individuality, must fight passion; the slave girl, of course, is not entitled to this privilege; it is denied to her, both by her society and her master; while the free woman must remain cool and in control of herself, even in the arms of her companion, to avoid being truly "had," the slave girl is permitted no such luxury; her control is in the hands of her master, and she must, upon the mere word of her master, surrender herself, writhing, to the humiliating heats of a degraded slave girl's ecstasy. Only when a woman is owned can she be fully enjoyed.
Tribesmen of Gor    Book 10    Page 17
He had taken my virginity; he had taken much pleasure in me; he had won me, forcing from me my total surrender as a slave girl to his power; then he had permitted his men to amuse themselves with me.
Slave Girl of Gor    Book 11    Page 87
Yesterday night my master had taken my virginity, much pleasured himself with me, and forced my total surrender to him, the surrender of a completely vanquished bond girl.
Slave Girl of Gor    Book 11    Page 99
He toyed with her resistance, sometimes permitting it to become stronger, sometimes even letting her think she might be able to withstand him, but then again he would begin to induce in her, subtly, the surrender spasms of the female slave. She well knew he was playing with her. "Beast," she wept, "how long will you sport with me?" Many times he brought her to the verge of surrender, teeth clenched, eyes shut, and then let her subside, retaining yet, to her cruel disappointment, a shred of her Earth-girl dignity.
Slave Girl of Gor    Book 11    Page 407
She had heard, an hour ago or so, Sasi's cry, emitted in the throes of her first slave orgasm, acknowledging her surrender to me as a slave girl.
Explorers of Gor    Book 13    Page 95
"I had not known such sensations could exist," she had said.
"They are attainable only by the slave," I told her. "They are the surrender and submission spasms of the owned woman, the girl who must yield absolutely and totally, holding nothing back, to her master."
Explorers of Gor    Book 13    Pages 364 - 365
In all fairness, though, one must note that there is a large variety of slave dances on Gor, and that there is some variation from city to city. The institution of female slavery on Gor is doubtless thousands of years old; accordingly it is natural that there should be great complexity and refinement in such a delicious art form as slave dance. There are even, it might be mentioned, hate dances and rebellion dances, but most dances, as might be expected, are display dances, or need dances, or love and submission dances; even the hate and rebellion dances, of course, conclude, inevitably, with the ultimate surrender of the girl to her master as a love slave.
Fighting Slave of Gor    Book 14    Pages 288 - 289
Slave girls must yield, and fully, to any man. Their entire mental set, so to speak, in the furs, is oriented toward providing the master with marvelous pleasures, and, in their own case, to feel as richly and deeply as possible, and, in the end, in an uncompromised and delicious capitulation, submitting fully to their master, to obtain the surrender spasms of one who is merely a vanquished woman, naught but an owned and degraded slave.
Savages of Gor    Book 17    Page 221
"Sometimes one tries different things," she said, "for example, about or on the furniture, on the floor, about their bodies, at their feet, on your back, on your belly, hoping to find something that they will respond to. Sometimes they give you explicit instructions or commands, as when a woman is put through slave paces. Sometimes they guide you, or help you, sometimes by the whip, sometimes by expressions or cries. At other times the girl listens, so to speak, to the slave fires in her belly, and seems to become one with them and the dance, and then, soon, must beg the brutes, in her dance, and by her piteous expressions and gestures, to relieve the merciless tensions in her body, allowing her to complete the cruel cycle of arousal, allowing her to receive them and submit to them, the masters, in the spasmodic surrender of the helpless slave."
Kajira of Gor    Book 19    Pages 160 - 161
"Please have pity on me, Master!" I cried. "I acknowledge that I have been conquered. I am vanquished! I am now yours, and as you want me, as a slave, fully! I beg now only to be permitted to yield to you abjectly and shamelessly. Let me tender to you now the helpless surrender of an orgasmic slave!"
Kajira of Gor    Book 19    Pages 341 - 342
I felt then the raptures of my bondage, from the tranquillities of selfless service to the ecstasy of a slave's sexual surrender to the dominant male, the master.
Kajira of Gor    Book 19    Page 344
She was not trained. She did not know slave dance. Her movements were those of a virgin, a white-silk girl. She had not yet been taught slave helplessness. No man yet in his arms had taught her the exquisite, transforming degradations of the utilized slave, the wrenching surrender spasms, enforced upon her by his will, of the conquered bondwoman, experiences which, once she has had them, she is never willing to give up, experiences which she comes to need, experiences for which she will do anything, experiences which, whether she wishes it or not, put her at and keep her at, the mercy of men.
Players of Gor    Book 20    Page 20
"And do you surrender wholly to your masters, and yield totally to them?" he asked.
"Yes, Master," I whispered.
Dancer of Gor    Book 22    Page 249
Moving as she did, and being what she was, a slave, was the deepest and most wonderful thing in her being, and she reveled in it, and loved it! She had wanted only the clear understanding that she must now surrender to it, that she was now truly a slave. She was elated in the harness.
"There!" said the keeper, pointing out a fellow with the coiled whip.
Renegades of Gor    Book 23    Page 429
I then yielding to him my utter submission, my total surrender.
I could not help myself.
I was slave.
Witness of Gor    Book 26    Page 295
"I do not refer to the tamenesses, the banalities, the lukewarmnesses," I said. "I do not refer to the tepidities. I refer to perilous heights and formidable depths. I refer to matters of force and power, of storms and fire, of songs and blood, of shouting and crying, of laughter and tears, of realities, of victories, of dominance and submission, of owner and owned, of master and slave, of the joy and absolute and uncompromising conquest and the rapture of utter, unconditional surrender."
Witness of Gor    Book 26    Page 448
"So in your supposed carelessness, that having to do with your veiling," I said, "I see more than the cruel delight of an ignoble and petty woman, little more than a she-sleen, protected by the transitory artificiality of station, to torment men. I see, rather, a woman who is displaying herself, as a woman, before men. In your dreams did you not occasionally find yourself back-braceleted and naked in the arms of a master, knowing that he might, if it pleased him, and whether you wished it or not, force upon you uncompromisingly rapturous ecstasies, ecstasies in the throes of which you, at last, will beg to utter the surrender cries of the yielded slave?"
Mariners of Gor    Book 30    Pages 87 - 88
A slave may desire her master, long for him, want more than anything to surrender herself wholly and unquestioningly to him, ache for him with all the flames of love, yearn to submit herself to him as no more than a negligible, meaningless, helpless, loving beast, be willing to die for him, but, too, she may well fear him, for the whip is his, and he is master.
Conspirators of Gor    Book 31    Page 370
How radiant, how beautiful, was Paula! On Earth she had been nothing, and now, on Gor, she was the slave of a master. How she had longed for this world, and how she now found herself upon it, and as she wished to be, owned, and mastered, a branded, collared slave. Selflessness, and abject surrender, was her joy. Total and uncompromising slavery to her master was her ecstasy.
Plunder of Gor    Book 34    Page 564
My attitudes and emotions concerning him swept from pole to pole, from horizon to horizon, in gamuts ranging from stinging humiliation at how he had treated me, I, a woman of Earth, educated and intelligent, a former acquaintance, now half-naked, collared, and marked, now an abject slave at his mercy on another world, to an overwhelming, submissive awe at his manhood, his rightful power over me, from rage at how he had scorned and commanded me, handling me as though I might be no more than a domestic animal, to a slave's desire to surrender herself, flaming and begging, in tears, to his least touch.
Quarry of Gor    Book 35    Page 161