If you are going counterclockwise, the horse should be on their left lead, to support their weight properly and to be balenced. Vice versa for going in the opposite direction.
When my mare doesn't want to take her left lead (it is the side that she doesn't use alot when we are on the trail, since that is what I use her for prodominantly) I go in a smaller and smaller circle no matter what lead she is on until she switches onto her correct lead.
Shaneequah, 1998 gaited Bashkir CurlyxArab mare
Treyue, 1999 3-gaited Icelandic gelding
Loki, 2001-2015 Icelandic gelding