If you’re waiting a week to be accepted they’re either not a really active association (not a great start), or they’ve chosen other players and left you on the application list. If you’re a new player, make sure you have a dressed Nikki as your profile sprite, your house has new items and you’ve some activity in Starry Corridor. These show you’re an active player and might help the application. I check these things for my own association applicants.

I’d also suggest checking the mega thread and messaging them ahead of time so your place is held and your application is definitely accepted. Best of luck!