Common privet is very tolerant to pruning. You can cut back to as short as 10-12 inches and it will regrow rapidly, however that hard a treatment should be done while the plant is still dormant. You can still prune moderately at this time.

gardengal is, as usual, correct in that it's best to prune heavily (butcher, if you like) when dormant, but privet is so cast iron a plant that it can be done anytime, if you don't mind babying it a tiny bit - water and mulch. A couple of years ago, I cut mine down to little stubs, less than 10", and it was, and is fine. I keep hoping the hard winters will do it in, but no luck.
A word of warning - the interior main branches are TOUGH. Be ready for some hard sawing.

its a pretty aggressive plant .. for the spot the prior nimrod panted it ... probably requiring at least twice a year shearing.. to keep it in shape ... which of course they didnt do.. leaving you this nightmare

when i got my first house ... i was going to restore all the plants.. for the history of it all ... 5 years later i finally got rid of the last mistake the prior owners made... happiest day of my garden life at that house ...

get rid of it.. and plant your own mistakes .... lol ...

i live in snow country ... that is not a great place if you also have to shovel or blow snow... for any shrub ...

get rid of it.. and go back to grass for that spot ...

and just to get you mad at it.. i wonder if its the reason the blacktop is cracking.. not so much due to roots ... but to how its affects the blacktop in winter sun .... a repeated freezing and thawing in mid winter ...

i also wonder where you are ...

get rid of it ... lifes too short to waste time and effort on a common privet.. that is invasive in some areas ...

ken

Here in Wales there are privet hedges everyeveryeverywhere, often wildly overgrown, sometimes kept in perfect tidy order. I hate privet and have found it impossible to kill no matter how harshly I deal with it. I'm gradually removing them and replacing with a mixed hedge, but the ones I have left all got "pruned" (hacked) down to about 18" a few weeks ago, and they're merrily sprouting right back. Good luck.