The late arrival for the more exclusive/popular (famous) guests.
The term is both used to excuse late arrivals and practised to appear more popular, exclusive, busy and sensational.
BEN: Dude we're so fucking late!
JOHN: That's alright Ben, you know... fame delay. Am I right?
OR
BEN: Come on, let's go!
JOHN: No way dude! Don't forget about fame delay. We should at least arrive one hour into the party.
BEN: Oh yeah right. We're so V.I.P.!
FIONA: Omg guys. Stop being such assholes.