So I'm not sure of the species of this shrub but as you can see in the images a good portion of it has become brown and appears dead. Do I prune off the brown parts or do I leave it and hope they come back? I'm just concerned the shrub will die and admittedly do not possess the best green thumb so seeking advice from someone more knowledgeable.
Well, that was quick! Definitely cut the dead material out. Is this ONE plant that has died or is this a branch of the whole? I am guessing this is Taxus densiflora or Taxus c. repandens. A yew. The only conifer that thrives in shade. Very toxic, especially the berries just don't allow kiddies or doggies to eat it. Wonderful plant. When did you plant this guy? Cut that dead stuff out for sure. If anymore of that plant starts to turn brown let us know as that could indicate a larger problem. Otherwise it could just be a compromised branch that was broken or bent when planted or someone stepped on this guy.
Take a picture of that branch by pulling the foliage away so we are able to see where the dead starts and the live part ends. Use alcohol on your pruners before and after just in case this is a disease, you don't want to spread the disease nor do you want to inject a disease.