IN UNIVERSE
If you look at the rank insignia, Kirk has reverted to the Captain's insignia, rather than the Admirals insignia. This places it after the events of Star Trek IV, as Kirk had not been demoted yet. Combine this with Uhura's distinctive hair (As noted by @NKCampbell in comments and excellent answer), and you can place it after IV and before VI (as seen with Uhura's hair in this photo).

You can also look at the design of the bridge screens. As seen in this photo for the bridge for the Enterprise at the time of Star Trek IV, it is much more bulkhead and "TV" type screens:

Compare this with an image from the bridge during Star Trek V:

This image shows the captains chair with arms and angled controls at the end:

As compared to the captain's chair from ST III/IV:

OUT OF UNIVERSE
This is a publicity photo from Star Trek V: The Final Frontier.
The timeline for Star Trek at Memory Alpha gives the stardate as 8454.1, or Earth Date 2287.
So presumably, even though this is an out of universe publicity still, it is intended to be a voyage/mission photo from the shakedown cruise of the NCC-1701-A. (Much as NASA has been doing for decades) with a stardate as noted above.