Q.Conifers on neighbours side of fence take all moisture. What plants will tolerate conditions. Can I improve soil
On the neighbours side of the fence is a row of large, well-established conifers. Plants on my side struggle to survive due, I believe to the conifers taking all the moisture and nutrients. Is there anything I can do to improve the soil and what plants will thrive best in these conditions. The site on my side is open and sunny.

Certified GKH Gardening Expert
Without knowing the exact conifer in question, it will be difficult to say if there is any allelopathy going on. What I can say with some certainty is that the soil is more than likely very acidic. This is likely the reason that hardly anything will grow there.
What you can do is choose plants that will tolerate acidic soil. This article will help: https://www.gardeningknowhow.com/garden-how-to/soil-fertilizers/acid-loving-plants.htm