I suppose much depends upon how “tidy” you want it to look. Thinning and grubbing is probably the simplest answer.

This is a stand alone hawthorn that used to be a hedge plant. It just needed space. It doesn’t seed regen because I occasionally mow my side of the fence and my neighbour’s stock graze the other.
If I had space I would love a thorn thicket; so much goes on inside them.
Off topic but if anyone wants to grow up a hedge plant - make sure that your chosen leader starts below any stem that has been laid in the past to get a secure stable trunk.

pee ess,
My ancestors would warn you to be very careful before doing anything with blackthorn.

This is a stand alone hawthorn that used to be a hedge plant. It just needed space. It doesn’t seed regen because I occasionally mow my side of the fence and my neighbour’s stock graze the other.
If I had space I would love a thorn thicket; so much goes on inside them.
Off topic but if anyone wants to grow up a hedge plant - make sure that your chosen leader starts below any stem that has been laid in the past to get a secure stable trunk.

pee ess,
My ancestors would warn you to be very careful before doing anything with blackthorn.