If you want full maintenance/management of the MC Library on the HTPC NUC, and you don't want your primary computer to be running when you watch your HTPC, then you will have to use Windows Remote Desktop to connect to the NUC from your primary computer to do the maintenance. Or one of the other remote desktop solutions such as VNC, TeamViewer, etc.
The alternative is to use your primary computer as the MC Server, with media files on the NAS as now, and set up the HTPC NUC as a Client of the primary computer. Then all maintenance can be done on the primary computer. But then the primary computer will have to be running, or set to wake up, whenever you want to use the HTPC.
You can do some maintenance of a Library on the NUC acting as a MC Server from your primary computer acting as a MC Client, but not all. i.e. Not View maintenance, Importing, Get Movie & TV Info, any functions that involve file management such as Cover Art collection, Rename, Move & Copy Files, etc. A search of the forum would find lots of discussions and a more complete list of what doesn't work when using a MC Client to maintain a MC Server.