At one point in Star Trek Beyond, everyone fastened their seat belts. At last! Is this the first time in Star Trek (TV, movies) that seat belts have been used? If not, what was the first time?
Seatbelts feature in a number of Star Trek properties that significantly pre-date Star Trek Beyond.
You can also see that Archer's chair (which looks very suspiciously like Picard's unused prop from Nemesis) has been retro-fitted with slots for shoulder straps in Enterprise, albeit we don't see their use.
That all depends on your definition of "Seatbelts". The first bridge seat restraint system was seen in Star Trek: The Motion Picture.
On the Captain's chair, the seat arms folded down over the lap during emergencies.
In ST3:The Search for Spock, the crew of the Excelsior use some kind of seat restraint just before they go to trans-warp.
There were seat belts used in the TNG era as well as in the new, alternate timeline.
The alternate timeline version of the Enterprise has selt belts that sort of craw or unroll onto your body. There is a scene where someone is knocked out, put into a chair, and then a button is pushed to activate seat belts /safty restraints to avoid injury.
This GIF was the best one I could find, and happens to be from Valorum's answer. :)
One of the TNG feature films included a scene in which Ctp. Picard (and others) are strapped in use some sort of heavy duty seat belts.