Does your mare lunge well?
Put your mare in your usual lunging setup, whether it be a rope halter with a lunge line attached or otherwise. You don't need a long line for this, only long enough to have the horse trot a circle around you and enough left over line to use the end for forward.
Walk forward while holding the lead a few feet down the lead rope. You want there to be a nice drape at this point while you're teaching this. You also want to give your horse room to move. As soon as the slack comes out of the lead rope when she lags behind you, quickly turn around and send your horse off in a trot around you. Only ask your horse for a couple circles. You aren't lunging here, just teaching your horse to move forward off of that pressure.
Then ask her to stop, make sure she's relaxed, then walk off again and repeat the above. I find most horses pick this up very well in a single lesson.
Pick your stopping point when your horse is coming off that slight pressure when the slack starts to come out. When she's coming off that pressure, don't have her lunge
Over the next couple sessions you'll refine it more. Instead of having her stay at a nice pace behind you with slack, bring your arm forward a bit. This will start to take the slack out in the same way it did when you sped up. When she starts to come more forward in relation to you, bring your arm back to a neutral position. After she understands to come forward, every time she slips behind you, ask her to come forward again.
From there you can start to shorten your lead to a more showmanship appropriate length.