I train my driving horses dressage style, so I start out by asking them to go on the bit--once they have that then asking for the extended trot comes quite easily--I will ask the horse to move on, while at the same time feeling the reins a little more firmly. Don't pull, but tighten your fingers to "hold" her a little more as you ask her to move on. This will encourage her to extend, rather than just speeding up. It works better to ask for extension when the horse isn't too fresh, especially when you first start asking for extension. A horse that is fresh will be more inclined to just move her legs faster--if she has been working for a little while & is even a little tired, she will be much more inclined to do a real extension--really, it is less work to stretch the legs out a little more than it is to move them faster. Generally the first time I ask a horse for some extension it is at the end of a lesion, when he is no longer fresh. I'll ask once and if I get a few strides I will bring him back to a working trot, then ask for another extension & call it good for the day. Do not ask for a lot of extension to start with--be happy with a few lengthened strides, then bring her back and ask again after a bit. If you're working in an arena, only ask for lengthening down the long side--bring her back to a working trot when going around the ends of the arena. It will be much easier for her to do on the straightaway.
