If your ATV clicks when you try to start it and you buy a new starter will that solve the problem?

I would first check connections. Clean terminals, makes sure it has good connection between battery and starter, as well as fuse box. Then check battery, Even if it shows 12 volts, it may have no cold cranking power left in it. A simple way is to turn on lights, they should be bright. If they almost die when you hit starter, most likely the battery is bad, or starter is draining to much power. I would always check least expensive and easiest probable component first, (battery most likely) If the connections seem good, battery is good, then pull starter, take it down and have it bench tested. Good Luck