Seat belts feature in a number of Star Trek properties that significantly pre-date
Star Trek Beyond .
They were seen in a deleted scene from Star Trek:
Nemesis In Star Trek Into Darkness
Shuttlecraft also have them in various episodes of TNG
The Animated Series (TAS: "Once Upon a Planet")
during a gravity loss scenario .
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.
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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.
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In addition to the other fine answers, seat belts were used the first time humans achieved warp
( Star Trek:
First Contact ):
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In ST3: The Search for Spock , the crew of the Excelsior use some kind of seat restraint just before they go to trans-warp.
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#No
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 seat 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/safety restraints to avoid injury.
One of the TNG feature films included a scene in which Cpt.
Picard (and others) are strapped in use some sort of heavy duty seat belts.
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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?
Were seat belts used in Star Trek for the first time in Star Trek Beyond?
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The answer to this question depends on the definition of "seatbelts". The first restraint system might have been used in Star Trek: The Motion Picture. Furthermore, there were seatbelts or at least seatbelt-like restraints used in TNG and Enterprise  Views vary - it may be that Star Trek: The Motion Picture was the first time seat belts were used but they may also have been used ever since humans developed warp and both in the TNG era and the new timeline.
Depending on your definition, the first time was the bridge restraint system in Star Trek: The Motion Picture. Seat belts were first used when humans first achieved warp. The Excelsior crew use some kind of seat restraint just before going trans-warp. Seat belts were used both in the TNG era and in the new timeline.