Clover is a nitrogen fixing plant - used to be that you’d plant clover for a year in between other crops to make your soil fertile again.

(It’s the bacteria in the roots that do the actual nitrogen chemistry.)

Clover fixes nitrogen and roots help stabilize the voids in the soil. They sell seed mixes called "ground cover mix" that includes other plants and will help keep the soil from recompacting when it rains and keeps weeds at bay.

Really good advice above. But if you want to cheat a bit, I used https://www.thompson-morgan.com/p/vitax-clay-breaker--25-kg-... on my heavy clay garden and it helped a lot, in combination with extra organic material etc.