Valkris was a Klingon operative in the 23rd century, who was romantically involved with Commander Kruge.
In 2285, Valkris undertook a mission for Kruge to obtain information on the Federation technology known as "the Genesis Device." Hiring a merchant vessel to facilitate her mission, Valkris made contact with Kruge and supplied him with the data. When Kruge learned, however, that Valkris had reviewed the information herself, he destroyed her vessel in order to preserve the secrecy of the mission. Valkris excepted this without complaint and was told by Kruge that she would be remembered with honor. (Star Trek III: The Search for Spock)
Appendices
Background
Valkris was played by actress Cathie Shirriff. According to the script, she was described as an "exotically beautiful woman of epic proportions and mystery."
In Marc Okrand's tlhIngan Hol language, Valkris' name is valQIS. (The Klingon Dictionary 2nd ed., p. 58)
Apocrypha
In the novelization of Star Trek III, we learn than Valkris has an older brother, Kiosan. When she was chosen to lead her family's house over him, he fell into dishonor, and his behavior so tainted the family that she was forced to disown him. She undertook the mission to steal the Project Genesis data because she knew Kruge would kill her afterwards in a manner that would restore her family honor. There is no evidence of a romantic involvement with Kruge in the novelization; he admires her as a fierce warrior, and she "loves" him because he is her meal ticket to redemption. This point was not made clear in the film, most likely for pacing purposes.