At 7:00 you mosey on over to the restaurant. That's what happens.
Its no big deal...the park 'closes' at 7:00, but many stores and things stay open for like an hour afterward to catch people as they are exiting the park. You can get in line for a ride at 6:59, and they keep running the ride until everyone in the line has ridden. It's not like they kick everyone out on the chime of 7. So you have nothing to worry about.