It can sometimes be difficult to find games especially for younger children as it always tends to be the popular games that get advertised more so than any other games and these games tend to be for people much older such as teens or even adults. It all really depends on if you are looking for free or paid. I know some games are available as part of Apple Arcade which is a gaming subscription service which is $5 a month.
Run Sackboy! Run is a great game for someone of the age you are looking for and it's also FREE. This game is the mobile version of Little Big Planet. It's a runner platform game and in the game the player can run and collect, bubbles, coins and stickers which will increase your score through the level. Each level will give you more tasks, so it makes it different each level you reach.
Rayman Adventures is another game you could try with your child that they may enjoy. This game is also FREE! In this game the player runs through trying to find secret eggs that protect the sacred tree.
Another great one is Animal Crossing Pocket Camp. This one is also free and if you have ever heard of or seen animal crossing or even played it yourself, you will know how much fun can be had in this game.
I hope these have helped a little. I would definitely recommend looking into Apple Arcade though as there are a lot of games in there that are suitable for a 4 year old that would be worth checking out.
