Conditioning

I'm starting to ride a 15.3hh Appendix, only for a short while until my friend starts to ride him. I had my second ride on him today, and god he's just a lovely guy.
He's on the older side, though, about 20, but he has a lot of spunk!
Anyway, are there any good exercises I could do to help him get back in shape? He hadn't been ridden for a few months, and I'm not pushing anything, although he likes to go (however he's the most comfortable horse - walk, trot and canter, I've ridden...it's truly a great ride!).
He's always relaxed, however I'm going to ask his owner to put him on supplements or possibly bute. He's older, stiff and needs new shoes, but hopefully for the time being he'll be fine.
Feel free to ask questions if needed.
Thank you!

Trotting. Continues trotting. Some people think its when you go fast, [such as canter, gallop] that helps your horse get in shape, but its not. Trotting helps builds muscle. Just spend a little extra time trotting each day, it might take a while, but he will be in shape before you know it!

Thanks!

Trotting and circeling.
Trot more often and make 20 meter circles both directions this will build his balance, stamina, and muscle

Trotting, trot poles and uphill work :)

Consistent ground work is enough. Lots of trot and canter. Taking him on uneven terrain (hills) will help him build muscle while varying what you do with him. Adding poles and varying your ground work even the location of your ground work such as riding outside, inside in a grass ring if you have access to one etc.

Great work for an older fellow. Keeping him in good shape without pushing him will be great for him.

Thank you all - he's being very good lately. I'm just getting him ready for a friend that might start riding him, although he's such a good boy!