What kind of privet? If you posted a couple of pictures it would be easier to guess your situation, but you might try a fall (or now, winter) fertilization followed by very heavy pruning in the spring to allow more light to penetrate the privet. I did this to a worn out hedge only I decided to completely rejuvenate it by cutting it off about 8-9" from the ground. The results took a couple of years but paid off. If the hedge is too old to stand this treatment, it is probably time to replace with another shade and competition tolerant plant. Good luck!