I would try pulling her nose to the outside and asking in a corner or going in a circle to work on it.
My mare does the exact same thing, she used to play polo and her previous owner didn't really do any flatwork with her. Now I have to build her up again. Like Sofia said your TB is unbalanced, if you do a lot of trot work in circles it does help and my mare is becoming stronger on her right side. As soon as they become stronger you can work on getting that canter lead right.
Try more bend when you ask for the canter, or asking in a corner or on a circle so you have the bend. Make sure your signals are clear to the horse so they understand what you want.
It's probably because she isn't very balanced on that lead. It's common with ex-racehorses because they usually race only to the left lead. My OTTB wouldn't pick up the right either. Do lots of circles to the right on trot and do some lateral work. Ask for the canter on the right lead while lunging her then try while riding.