You will need a new grip, since your right grip is shorter than the left.
When replacing the grips, some things to consider:
A few boutique kids bike brands like Woom and Cleary use narrow 19mm diameter handlebars that require special grips. Most brands use a standard 22.2mm grip.
Kids hands are smaller, so try to get a grip that is a bit thinner. something like an Oury grip will be hard for a smaller kid to get a hand around
Kids handlebars are narrower width than adult bikes, so everything is close together. It can be hard to fit the new shifter, brake lever, and grip. You may need to cut the grip a bit to fit.
I had decent luck with these cheap Amazon grips, they come in a nice selection of colors.