In TOS, Checkov was a navigator. (His station was called "navigation" a number of times through the series.) When the Enterprise received her refit, Pavel transferred to operations department and became a security/tactical officer.
He spent some time as First Officer on Reliant (we don't know if he was also the security/tactical officer at the time) before returning to his former job on the Enterprise at the end of STII. In STIII, he doubled as the de facto science officer on the Enterprise's return to Spacedock.
In Trek IV, he was navigating the bird of prey (following the refit on Vulcan...again, we don't know if his station contained both tactical and navigational controls).
In Treks V and VI, Pavel was back at the navigation station, but he clearly also acted as chief security/tactical officer during those movies.
So, it appears that Pavel went through security/tactical training after the Enterprise returned to Earth to begin her refit. I further submit that the position of "tactical officer" was created around that time, and that Pavel was probably one of the first officers to go through training as a Starfleet tactical officer.
In ST:E, I haven't really paid attention to their navigational orders. There's probably some poor ensign offscreen, stuck in some cramped closet, with only a computer screen and the Vulcan star charts to keep him company, plotting all of the courses as per the captain's orders.
Davy Jones
"Frightened? My dear, you are looking at a man who has laughed in the face of death, sneered at doom, and chuckled at catastrophe! I was petrified."
-- The Wizard of Oz