1
general::
Curry favor with, flatter, as in There's no use playing up to the boss; it doesn't influence him. This expression originated about 1800 in the theater, where it meant "to support or assist another actor." Within a couple of decades it was being used in other venues.
American Heritage Idioms
2
general::
Phrase(s): play up to someone
to flatter someone; to try to gain influence with someone. • It won’t do any good to play up to me. I refuse to agree to your proposal. • I played up to him and he still wouldn’t give in to me.
McGrawhill's American Idioms And Phrasal Verbs