They can rent a private aircraft if they don’t own one.
As an airline pilot, we have the occasional celebrity on board. They usually travel in first class and they usually attempt to keep a very low profile by wearing big sunglasses and hats. The flight attendants always seem to be able to identify them though. The flight attendants often read the gossip magazines and know the whole back story of the celebs that board.
I have seen situations where the celebrity and their bodyguards are boarded first and sit in the very back of the airplane in coach. I don’t really know why they do it that way but I suppose it’s so the celebrity has less public contact. I remember we had Mike Tyson on board one time many years ago and he had some body guards and others with him who camped out in the very back of the airplane. I also had Alan Greenspan, the chairman of the Federal Reserve at the time, who traveled with some secret service folks in coach on a shorter flight. He was considered a rock star at the time so I shook his hand as he got off.
I can’t remember her name, but there was a famous actress who was aboard one of my flights and she was driven to the gate from a private lounge in the terminal. She boarded last in first class but I don’t know what happened when we landed. I suppose she walked off into the terminal like everyone else. Most airlines keep a small private VIP room where people who can’t be in public can wait for their flight. I’ve been inside ours and it’s nothing fancy. You enter it from an unmarked door and it just had some seating and a screen showing the departures.
I don’t fly longhaul overseas but those crews tell me that they often have celebrities and it’s a pain for the cabin crew because they can be demanding or so reclusive that they can barely communicate with them.