When that happens I just destroy the items I won’t ever use or the one cheapest ones like 60 coins. You can also go to the store in Hogsmeade and sell them. To get more gear slots you need to do Merlin Trials.
There’s a quest around Hogsfield where you can start/learn about them.
The greatest thing is you can wear your best gear and don’t have to worry about matching. If you hover over each gear slot and press F (it’s F on PC I’m not sure what it is on other consoles, but it should say change appearance), you can wear whatever you want without worrying about defense/offense. It acts as a sort of mask on top of your gear. And whatever you’ve already collected stays in that catalouge. So if you get a cute worthless hat, you can sell it and still wear it.