I have an older 500mm F4 AF-1 and a newer 300mm f2.8 AF-S.
The 300mm f2.8 takes 52mm filters and I think your 200-400mm lens will also take 52mm filters.
I suggest that you purchase Nikon filters as these filters are of a "thinner" construction, compared to a "Hoya" for example.
You may find that some filters are too thick to drop into the slot when assembled into to the carrier. Of course, you could go to the trouble (and expense )of having thick filters machined down, but, that is somewhat impractable.
If you are looking for a circular polariser, I feel the Nikon C-PL 1L may be the correct unit. This one fits my 300mm f2.8 AF-S. Best to check first though if you want to purchase one.
Nikon manufacture "drop-in" filters in 39mm and 52mm sizes. The 39mm is for some of the older lenses, such as my 500mm f4 AF-I.