Do you mean a Leyland Cypress? They sure do take up a lot of space, don't they? Yes you can trim some of the lower branches. Not more than 1/3.

How high (and how thick) is your hedge and what do you plan to do with the reclaimed space?

What is on the other side of the hedge? Is there a fence or wall? Otherwise, removing lower branches will lead to big gaps between the trunks which will affect the wind flow across the rest of you garden. (A photo would be useful)

Planting under a Leylandii hedge is a challenge - try an Internet search for "planting under Leylandii".

You can take the whole branch off to the trunk, if that's what you mean. If you want to cut the branches back half way remember that if you cut back beyond the green they will never green up again.

Put lots of good mulch - whatever you have to hand - on your border before planting anything else in it.

I meant don't remove more than 1/3 of the branches.