There's a lot of potential configuration issues, from firewall (on your NAS) to Plex server setup. I'd err more towards asking on a Plex forum as it's unlikely to be an issue with the router itself, especially as it's on the LAN side.

One thing to check, you've installed Plex server on the NAS, I assume?

  @richpriest My NAS drive isn't great, but it does what I need. It doesn't have many options, so not sure if I can access firewall settings. I'm not sure if putting the Plex server on it will work. Obviously I can put the software on there, but I don't think I'll be able to open it from the drive. I'll try the Plex forum as well. 

  @richpriest I've been using the Plex server on my Mac, which is on the same network as the NAS drive. I can link the files via my Mac, but I want to be able to do it directly from the NAS drive. 

So you have two options with what you have currently:

A) Install Plex server on the NAS and have the Plex client connect to that

B) Attach the media shares from the NAS to the Mac's Plex server's media library, and have the Plex clients connect to the Mac. You'll need the Mac switched on when you want to use Plex for this option to work.

  @richpriest Ok thank you for your help. I'll give it a go.