Yes... but with discretion

"Lady Trina," you say to her, and it surprises you that you are only barely able to keep your voice from squeaking! "You will be competing in the swordplay competition, is that not so?"

"Indeed I will, Sire," she says, her voice also level. "I must take my leave at the conclusion of the smithing contest, that I may prepare."

Your mind races... how to say something without actually saying anything? You glace over toward the area behind the stands where the contestants ready themselves with last-minute practice and other exercises, imagining how the young maidens will be standing around watching as the men in gleaming armor show off their skills, hoping to gain favour from one of them - and then, a thought comes to you.

"Lady Trina, please do not take offense at what I say now, but I imagine none have offered you favour for the contest; is that so?"

"It is so, Sire. Neither the men nor the ladies care to give a token to a swordmaiden; the former would find it belittling, and the latter would find it scandalous, or at the least inappropriate."

You quietly take a deep breath. "Lady Trina, one of my Kingsguard should not be so dishonored. I therefore would offer you a favour myself - one which you should not feel obligated to accept, but it would please me if you did. It need not be a public display; if you prefer, I will give a token in private and you may wear it privately."

Trina hesitates just a moment... and then, in a voice which is quieter than usual, she says, "I would be honored, Sire."

"Would you have me make the offer now?" you ask, as you re-enter the tournament stands, for a moment out of sight of any curious eyes.

Trina is quiet again for a moment, and then she seems to straighten herself with an inner resolve, turning to look you in the eye. "To receive favour from the King is not something for which one should ever feel shame," she says firmly. "If it please the King, I will receive any token you may offer in full view of the people and guests of Elyssia, and wear it proudly as I fight for the honor and glory of the Kingsguard. I have spoken, Sire."

"Then, so be it! And... thank you, my Lady, for allowing me this."

Trina opens her mouth as if to say something, but then stops; she may be blushing slightly, but in the dim light you cannot be sure. She then bows her head, and you both continue up the steps so that you may resume your seat.