Recently acquired horse with stiff rear leg from old tying injury. Noticeable at walk, not so much at other..?

As long as you don't have stifle injury, here are some things that can help:

Massage, either an equine massage therapist (yes, they are out there; my best friend is one) or work it yourself

Massage both sides.

Hand walking. Particularly up and down hills. Also, back the horse gently up a hill a couple of times a day. That gets the hip muscle into good usage as it has to flex and stretch deeply. If you are talking about lower leg, use some support wraps.

Heat therapy. Rub on heat that doesn't burn the hide. Warming therapies of any type.

If you are really dealing with muscles and not an injury in the lower leg, the fibers most likely have some scarring, but, yes, you can still break some of that up, get the muscle stretching, etc.

Take some video of the stride and after two weeks of therapy walking and massages, take another video. Often you will visually see a change within a few days.

As far as a slight gimp for 4-H, as long as the horse is not in pain lame, and the issue has vet clearance, it can compete. My daughter showed a tb that had a prior fracture and was nerve "clipped" and had a slight gimp on that fore. She still trophied on him in 4-H and local shows and even at state fair.

Edit: My daughter's horse was not showing symptoms of lameness. He worked happily. He just had a gimp from the prior injury. So if you are talking about a stiffness or muscle memory and the horse does not indicate pain, get the vet statement. There is a difference in one with current lameness and an old healed injury. You can show the latter. And that horse's limp was obvious to any trained eye. It never kept the two of them out of ribbons. He was a happy worker in the arena for her, and placed in the top ten in hunter jumper at state fair one year.

Im in 4h right now and And horse that shows signs of injury or appears to be unsound, they will disqualify. And I do Agree, get a vet out there, if it was a pulled muscle, it would have most likley healed, there might be a underlying probelm to her limp.

4H doesn't allow you to show lame horses.

I'd suggest getting your vet out. He can evaluate her for possible therapies, and if he thinks she's okay to show he can write something out for you. If it is a "fixed" problem, like a fused joint or shortened tendon, likely she'll be useable because using her bad leg doesn't hurt her or damage it.

I wouldn't rely on what the previous owner says the previous vet told her many years ago. I hope she was free?

i would get your vet out for a second opinion, If theres a noticable limp a judge Even in 4H will disqualify them and ask you to leave the arena. depending on how bad the limp is you may be asked to take the horse home before it even enters the arena.