You never know.
If this new movie does as well as it looks like it is going to, there could be renewed interest in all things Trek, and it could happen.
I don't remember any fan effort to get TOS remastered, so maybe the same group will go ahead and do TNG, too.
A lot of work went into TOS-R, but it was nothing compared to what TNG would entail. With TOS, they had completed, edited episodes on film they could tranfer from. With TNG, they would have to recreate every episode all over again using old film they'd have to sort through. What may happen is you have a bunch of film from a particular episode, much of which wasn't used, some of which was used, a some of which may be missing or damaged. It's unlikely the finished episodes would completely match the originals.
That said -- I didn't answer your original question -- there was talk about Paramount doing some sort of test, perhaps to see if they could enhance the resolution of the original episodes somehow. I'm sure there's interest in doing a TNG-R, it just may be a huge costly long-term nightmare to get it done. I'm sure something will happen eventually, but Paramount may decide it's going to have to wait a few years. They're going to have to figure out how to make it cost effective. Like I said, a TNG-R would be a far far bigger challenge than TOS-R was.