Accessories and their attachments, mounts, holsters, etc. are neither my primary interest or expertise, but I do get asked about them regularly, so I wanted to take a look at these in relation to the TNG jumpsuits themselves.
The primary accessories that characters might equip themselves with were tricorders (standard or medical), a Type 1 hand phaser (aka “cricket phaser,” mostly seen during the first two seasons), and/or a Type 2 phaser (first the “dustbuster,” later the “cobrahead”).
With the exception of the “cricket” phaser, which devices went on which side was inconsistent – presumably left up to the individual wearer in-universe and/or actor in reality.
Type 1 "Cricket" Phaser
As best I could determine, the “cricket” phaser was consistently worn on the wearer’s left side.
Worf’s “cricket” phaser was positioned considerably higher up his side than everyone else’s, presumably so it would be accessible above his baldric.
The “cricket” phaser holsters were slightly trapezoidal pouches made from the same jumbo spandex as the jumpsuit body, hand-sewn to the jumpsuit.
However, observe that while Worf’s was cut on the straight grain, these two “cricket” phaser pouches were cut on the bias (and opposite biases, at that):
Hand-sewing them to the jumpsuits allowed them to be added and removed as episodes and scenes demanded; they certainly weren’t present on all of the jumpsuits, all of the time.
However, it does seem that fairly early into the show, these “cricket” phaser pouches were deemed unintrusive when empty and unused, so they were left permanently affixed to some of the jumpsuits.
The “cricket” phaser pouches eventually became less common as the phasers themselves did – but we’ll circle back around to those shortly.
On the screen-used Worf TNG jumpsuit I examined, the long edges of the “cricket” phaser pouch were 3 ¾”, the wide (open) end was 2 ¾” tall, and the narrow (back) end was about 2 ⅜” tall.
Captain Picard
The Type 2 “dustbuster” (and later, “cobrahead”) phasers seem to have been positioned on whichever side the wearer preferred; Captain Picard wore his on his right side.
Commander Riker
Commander Riker usually wore his “dustbuster” phaser (or tricorder) on the right, as well.
However, on at least one occasion, he wore his phaser on his left side in favor of wearing a tricorder on his right.
Data
Data carried a tricorder far more often than a phaser, and he preferred to wear the tricorder on his right side.
On the occasion he did carry a Type 2 “dustbuster” phaser, he wore it on his left and continued to carry the tricorder on his right.
Worf
On the other hand, Worf armed himself far more often than he carried a tricorder, and he preferred to wear his “dustbuster” phaser on his right side.
On the occasion he did carry a tricorder, he seemed to prefer wearing it on his right side as well.
Geordi
Geordi seemed just as likely to carry a tricorder as a phaser, and he usually wore them on his right side.
On the occasion he carried both*, he carried his phaser on the left and tricorder on the right.
* In the “Shades of Gray” example above, he was actually carrying a sample container, not a tricorder.
Tasha Yar
Tasha usually preferred to wear her “dustbuster” phaser on her left side; when she carried a tricorder, she usually wore it on her right side regardless of whether or not she was also armed.
About two-thirds of the way into the season, though, she wore the two reversed a couple times.
Dr. Crusher
Naturally, Dr. Crusher often carried a medical tricorder, although she seldom actually wore it on her uniform; she’d typically hold it in her hand when beaming down and then carry it around (Gates McFadden is said to have loved playing with props), or the tricorder would be included in her over-the-shoulder medical kit.
She also sometimes carried her tricorder in the pocket of her lab coat.
When she did wear items on her uniform, for the first few seasons she wore her tricorder on her right side and her phaser on the left.
During the later seasons, though, she seemed to prefer wearing them the other way around (phaser on the right, tricorder on the left).
Counselor Troi
Counselor Troi seldom had occasion to wear either device with her TNG jumpsuit, but when she did, she wore the phaser on her left, and the tricorder on her right.
Supporting Characters
Both Ensign Ro and Commander Shelby also wore their phasers on the left, and Commander Shelby wore her tricorder on the right side.
Extras
Broadly speaking, extras (most commonly “goldshirts”) usually wore their phasers on the right side.
Although the majority of “goldshirts” tended to wear their phases on their right, some did occasionally wear them on the left.
Curiously, every member of Geordi’s ill-fated away team to the Tarchannen III outpost wore their “dustbuster” phasers on their left.
There were even occasions in which two extras wore their phasers on opposite sides, in the same shot.
These aren’t “continuity errors,” per se, since their orientations may well have been left to the preference of the wearer in-universe, but I thought it worth mentioning.
For what it’s worth, extras seem to have usually worn their tricorders on the right (see below, left and middle), but Lieutenant Commander Darren’s away team all wore their tricorders on their left (see below, right).
Holsters and Velcro
Unlike the smaller “cricket” phasers, the tricorders and larger Type 2 phasers were carried in separate holsters.
The holsters were attached to the jumpsuits via small patches of black hook-and-loop tape (“Velcro”).
These Velcro patches were presumably hand-sewn to the jumpsuits so they could be easily removed when they weren’t needed, but sometimes the unused patches were left attached and visible in the show.
Here some close-up auction photos of the Velcro holster patches on the jumpsuits.
Note that the jumpsuits pictured below actually have Velcro on both sides – perhaps so the wearer could put their phaser or tricorder on whichever side they wanted, or because the wearer was equipped with both.
