Hello liamr,
The amount of RAM you have should be plenty for whatever type of gaming you're into. Your graphics card seems like it too should be able to do a decent job and handling games. Your processor isn't bad, but there certainly are better ones out there. The problem is that processor is a socket FM2, which means if you want to upgrade you'll have to purchase another FM2 processor. In my personal opinion, I don't think it would be worth upgrading your processor. I don't think you'll see that big of a performance gain.
The best option would be to research gaming rigs and the type of processors their using. Based on that research, you'll probably have to upgrade your motherboard as well.
The good news is your other components are new enough to carry over to a new board, should you choose to go that route.
Let me know what you come up with.
Cheers!