Is it Party President or Party's President?

Is it only a matter of common usage/choice, or is one more appropriate than the other in certain cases?

'Party president'. Inanimate nouns do not usually assume a possessive form. Simply use the noun as an adjective-- here, modifying 'president'.

PS: I see this is your first post, Sunu. Welcome to English Forums. I hope you find us useful and enjoyable.
Thx MM.

Great to be here!