To play old Nick's advocate, "Navigator" might be an anachronistic name for a modern profession, the same way "Records Officer" in "Court Martial" seems to be some sort of a computer wizard who won't be spending any of his valuable time maintaining the ship's records.
That is, rather than find the quickest route from A to B, Chekov might concentrate on monitoring nearby traffic, adjusting the navigational deflector to balance protection-of-ship vs. drag-induced-by-deflection, or running the sensors that tell where A and B are in the first place. Or whatever.
Just about the only insight we get into Chekov's line of work is the instance or two when he's told to "calculate a spiral course" or "lay in a parabolic course". But even there, it seems the choice is made by the CO, and Chekov (or sometimes Sulu, directly) just punches it in - his role above and beyond feeding the automation with the skipper's command is still a mystery.