If you are removing a strip of drive to introduce a hedge, you need to ensure that any sub -base under the driveway surface is also removed and a good depth of good quality soil installed. The other thing to be aware off is undermining the edge of the driveway, if you have a tarmac drive a new edging will need to be installed, the most cost effective edge would be a concrete edging strip but this would need properly installed and set in concrete to ensure stability. I would suggest Griselinia littoralis which is an evergreen shrub with very consistent fresh green foliage year round. It's also drought and pollution tolerant; this garden below is on the sea front and is regularly exposed to salt spray and it thrives! Hope this is helpful?