If you outstay someone, you stay in a place longer than they do. Guests may outstay other guests at a party. There is a set phrase you will meet: to outstay your welcome. That means you stayed so long that people, though they were kind at first, now wish you had gone. The everyday way to say the simple idea is stay longer than. Outstay is a little more formal, and it often carries that extra feeling of “a bit too long.”