1. tv. to accompany someone [musically]. I have to sing a solo at a wedding and need someone to comp me.
2. tv. to give something to someone free. (Either as compensation for difficulties endured or as a complimentary gift.) The movie patron was angry and demanded his money back. The manager comped him with a few free passes and he was happy.
3. n. a complimentary gift. I expect comps when I spend a lot of money in a casino.