If this is an old video you need to redo it. Follow the same format. Then you can make a good comparison of then and now.
From the video posted, you need to have your vet look her.
Before you do get her trimmed up to anatomical correctness and remove any "action devices" (including heavy or weighted shoes; I could not tell from the video if, or how, she was shod). If she's trimmed "long and low" then it will take several weeks to several months to get her grown out to where she needs to be.
My layman's guess is a hock issue, probably arthritis. How old is she? She lookes shorter in the back to the right than to the left. She has no overstride (understride looks 6-12 inches, varying somewhat).
Conformationally, she's long backed. Can't tell about the rear legs but they look OK. Her topline is poor (that can be remedied with work). Bottom line better but still needs work. Nice back end; a little light in the front and neck.
Gait is pacy, but that too can be remedied with some conditioning and training. Looks like she tried to canter a couple of times but didn't make it. That, again, is suggestive of hock issues.
Generally, as noted in the thread below, gaited horses (particularly TWHs) are not notorious buckers. They can, they just don't usually. When they do it's a sign of something pretty significant. Let the vet do an eval. and then be guided by what they find.
Good luck with her!