As for new arrivals? Depends, I've had some that ate the very same day they arrived. Others it took a couple of days, one took a week, another went on a food strike for 3 weeks (turns out she was ovulating, she's eating now).
Some of mine ate the first time and some didn't. Funny thing I got 3 new ones in yesterday and the 2 youngest ate everything I gave them the first night and the oldest has not eaten yet. It just depends on the leo.
I got mine from a reptile show, and he had no problems eating, he wasn't fond of crickets at first, so stuck to mealies till he was ready. Now he'll eat both without any problems. He loves hunting for either. When I say that, I mean he'll go to the mealworm dish and do his little funny stance, I call it the Hunter Stance, and get all excited at mealtime! It's so funny to watch him eat!