Technical question
 

Hi everyone, new user here. I bought a scoot with a 157QMJ for dirt cheap since it wasn't running. The guy who sold it told me it had lost compression, which it hadn't, but it did have lots of other problems. A new one I found was that the kick start would get stuck and not go down well, or not return. I found that a few of the teeth were broken off the gear that is between the kick start shaft and the variator shaft. (Sorry, I haven't learned the proper names yet, which brings me to my question.)
The broken teeth look like they have trashed the teeth on the gear on the variator shaft (see pic). What is that gear called? I have seen a couple vids showing to use a bearing puller to get it off, but how would I put a new one one?
Thanks for helping out a noob ;)

The new gear just presses on. When you tighten the variator it will press that gear on to the tapered part of the crankshaft. Make sure when you put the new gear on the tapered cut goes to the inside