In a gated community, if unlicensed driver or with an expired license is admitted into the community and this driver has an accident, is the community or HOA liable?
Almost certainly not (Not without some important additional act that you haven't mentioned).
No. But it might not be a bad idea to call law enforcement if such behavior is observed, just to keep anyone from being able to claim that the behavior was condoned by allowing them through a manned gate.