It seems that Starfleet ships have a need to align their onboard clocks with some broader sense of official Starfleet time. I'm interested in why this is needed & how it works.
As an example, in "Clues", Star Trek: The Next Generation: Season 4, Episode 14, the Enterprise traveled through a wormhole (*) which transported them a distance equal to about 1 day's normal travel.
Upon realizing this Data suggests an operation to re-align the ship's clock:
PICARD: Thank you, Mister Data. Well, where the hell are we?
RIKER: Point five four parsecs from our original position. Almost a day's travel in just thirty seconds?
DATA: Sir, I should re-align the ship's clock with Starbase four ten's subspace signal to adjust for the time distortion.
(emphasis added - source of transcript)
Maybe there are other examples in other ST episodes, but I couldn't think of any.
In general, what is the purpose of this procedure? Why does Starfleet need to align their clocks based on their local position?
Actually they didn't, but at the time of the quote most of the crew thought they had and would have been following procedures accordingly. Also, although this may have been a step taken by Data to aid the cover up of actual events, nonetheless it must still have been standard procedure in order to not raise suspicion.