Pruning hackberry tree
How late in the season can I prune hackberry tree back to the main trunk?
Hennepin County Minnesota
The first reference below covers pruning Hackberries. It isn't clear from your question what exactly you wish to prune. Branches up to an inch in diameter can be pruned any time. It is best to prune large branches during the dormant period - winter, early spring.
You can read the recommendations and decide when to prune whatever it is you want to prune.
The second reference (U of M) refers to how to prune branches emanating from the trunk on any tree. You probably already know that and didn't ask, but it won't hurt to send it along.
This last reference is a description of Hackberry Witches Broom. Again, you didn't mention that but might find it interesting and will now be prepared if you ever see it on your tree.
You are to be commended for taking good care of your Hackberry. They do need to be pruned, as you know. Often they are not.