When your transition is solid and your horse responds well to the cluck, you can try to shift sides.
I switch rein and put my horse on a left canter on another circle, riding a figure eight right back to my canter transition spot.
I make an easy canter transition by slowing to walk and after a few steps, near the transition spot, I ask for the right canter.
Keep trying this and slowly reduce the amount of steps between the transitions, until there is no steps of walk only one canter to the other.
Be sure to give your horse plenty of breaks so they get the chance to digest the new things you’re teaching them.
When something went well, I often dismount and make that the end of the lesson, rewarding and patting the horse a lot to give him a sense of accomplishment.