What to do with nest!?

Hello! 

Recently we started trimming back our hedge, much to our surprise we found a active nest! We stopped trimming and left the hedge/nest alone all intact (yesterday morning). There were 3 beautiful blue speckled eggs inside (i believe either blackbird or robin eggs). This morning I checked on the nest and there is now only 1 egg left! What’s best to do? Leave the egg/nest alone, or try and move the nest out of potential predators reach?!

thanks!