I started climbing at 55 and I was 40 pounds heavier than I am now. I had problems with my elbows. I found icing them helped, and I did forearm strengthening exercises that didn't stress my elbows. I put a weight on a rope and tied it to a broomstick (cut short enough to hold in both hands). I would roll the rope up and down. It didn't take much to make my forearms burn, and it really helped in the long run with not straining my tendons in my elbow. (By the way, stop when it becomes too hard. You don't need to do it a lot of times, but doing it a little every day will help.)

I have osteoarthritis (bone on bone in both thumbs), so these days I have to tape the hell out of my hands to climb, but I don't have trouble with my elbows.