Royal Torment by Viola Grace

Running into a male entering rut gives her the opportunity to save her friends from punishment at the hands of the emperor. It isn’t really a hardship.

Tydella is the imperial princess. The only imperial princess. Her father had one daughter by her mother and refused to have any other children. He is a man of his word.
Tydella travels with ambassadorial duties and spends her birthday on a space station with her guard crew. She learns something that endangers her travelling family and decides to get into trouble to distract her parents from what her guards have been up to.

She heads out of the station on her own for a few days of unrestricted solitude and runs into one of her father’s people while clearing customs. He’s tall, he’s handsome, he’s stripey, and is going into rut. She can smell it. Their eyes meet, but she turns and takes off, waiting for a large ship to stick to in order to run through a gate without registering her location. She just happens to pick his ship.

Ador is fascinated by the sprightly woman with flashing eyes and magnificent attributes. He is disappointed that she slipped away from him at the station and beyond fascinated when he catches her magnetized to his ship. He offers her a choice and is stunned when she agrees to help him work off his rut.
She gets a vacation, he gets a partner, what could possibly complicate things?