Climbing

I read some advice somewhere where someone suggested to do continuous fall practice on the first route of the day. e.g. When you're at the third clip do a fall right at the clip, then halfway to the next clip do a fall, then at the next clip (before clipping in) do a fall. I think this should get you over the fear of falling, at least for that session

Find routes that you can climb in 2-3 attempts in redpoint style and climb to the fall on each attempt. Only move to a knew route when you climbed it or it is really to hard. After a time you get confident with falling

Lead more, or toprope but ask your belayer to keep a bit more slack once you're up a bit on the wall

I dont think you ever really overcome that fear. It is like a muscle you have to continuously train.

It's totally normal to be afraid to fall, especially if you just recently got certified. The best way to overcome that, is get used to that feeling by practicing.

When I started climbing again a few years ago, I made the same conclusion as you: there was a full grade between my top rope and lead climbings. At this point I decided to simply stop doing top rope entirely, to get used to lead. It took months, but it worked great ! I took many falls of course, and sometimes forced myself into trying moves even though I knew I would fall (rather than asking my partner to catch me).

This is the best advice I could give you: only do lead climbing for a few months, until it becomes natural to you, and take a moment after each fall to appreciate how smooth it was :)

And just so you don't feel too bad about it: you will always be scared to fall, it's natural, especially when you're above the clip, and not sure about your move. But at some point, you will simply be confident enough to go over it, and trust your fingers and foot more than your brain!

Exposure therapy. The more falls you take, the less anxiety you'll feel when facing the next fall.

Unfortunately, the fear comes back over time if you don't take falls, so you need to keep doing it. As they say, if you're not falling, you're not trying hard enough.