Welcome to the wonderful standardbred breed! I love this breed and I am currently riding two. I have some ideas but I am sure the experts will be along shortly.
I would first advise you to slow down a bit. I have one horse that was taught to canter in a traumatic way. He was put on a short lead and hit with a lunge whip repeatedly until he cantered. That resulted in him being a bit of a nightmare on the lunge line, terrified of the lunge whip and forgetting that he could trot and not canter all the time. I would not advise teaching your horse this way.
The other gelding I did not think had been taught to canter. I spent most of the summer working him at a trot and establishing a nice steady trot rhythm. He build up muscle and started to offer a canter. I rewarded that but I am not at this time asking for a canter because the trot is not 100%. It can be tempting to run before you can walk. That's true with any horse, so make sure you have the basics established.
I would ask how old your horse is and how long they were at the track? The longer they were at the track the longer they were told that cantering is a big no-no. Which means you are going to have to tell them that cantering is a big YES. So, don't rush because this is something that will to some degree blow your horses mind. I have a horse that raced for 14 years, asking him to canter would blow his mind to a point where the rewards are probably not worth the efforts. He does not even canter out in pasture he just racing trots (he is faster than the ones that are cantering too).
Once they have an established and nice trot. A fast trot and a slow trot and they are following a circle well, I would ask for the canter. This may not be comfortable as they will probably try a racing trot. Keep asking. When they canter relax and go with it, don't pull them back or correct for a few strides. Most standies have a lovely canter. The other option is to take them out on a trail and just ask them for a canter on a straight away. A lot of people have mixed feelings about that idea. No matter what you do I think the important thing is that they have a solid trot before asking for the canter.
There are also a few books and articles offered by the Standardbred pleasure horse organization of New Jersey on this very training issue. The SPHONJ has an online link to an article on there website.
Sorry for the novel!