Hi Kandy and welcome to Goy, I think you will have a problem growing anything under a privet hedge as they are gross feeders and will strip all the nourishment from the soil even if you add compost.

I moved to a house with a big privet hedge on one side of its garden and was surprised to find that Dicentra eximia was growing well under it. I thought, like Moongrower, that it would be a "dead zone". Maybe it got established before the hedge grew too big?

Ground elder likes the poor, dry soil conditions - but you might not want to hear that.

Would be interesting to know Beattie... I'm just glad we yanked ours out 15 years ago, maybe even more. Gave us another 5 foot of garden. We replaced with a fence which is now covered in Clematis alpina, winter flowering Jasmine, honeysuckle and a grapevine which never flowers!