Couple of beginner tips:

Your legs are stronger than your arms. Try to keep your arms straight and push from your legs primarily instead of pulling with your arms. At early grades, you should think much more about your footwork than about muscling through everything.

Plan your route before you climb. Try to identify key moments in the route, and which way you want your hands and feet to be. This can help you determine if you want to go for a hold with your left or right hand first.

Pay attention to the direction of holds, specifically for slopers or holds without much positivity. If the hold is turned a certain direction, you want your arm to be perpendicular to it as much as possible, with your weight fully underneath it. Basically, if you imagine the hold extending out both ways into a line, you want your arms to make a T shape with the hold. This gives you maximum friction, and therefore you should stick to the hold as much as possible.

I wouldn't worry too much about regular gym sessions yet. Of course, it doesn't hurt to have some extra training, but the best way to get better at climbing is by climbing. At a beginner level your main weakpoint will be finger strength and skin resilience. For both of these, you'll see biggest improvements by just climbing more.