To add to Valorum's answer. She's assigned to a science vessel to catch up on 300 years of...everything.
GILLIAN: I'm so happy for you, I can't tell you! Thank you, so much.
KIRK: Wait a minute! Where you going?
GILLIAN: You're going to your ship. I'm going to mine. Science vessel. I've got three hundred years of catch-up learning to do.
KIRK: You mean this is ...goodbye?
GILLIAN: Why does it have to be goodbye?
KIRK: Well, like they say in your century, ...I don't even have your telephone number. ...How will I find you?
GILLIAN: Don't worry. ...I'll find you. (a kiss) See you around the galaxy.