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Rear admiral was a flag officer rank above commodore but below vice admiral. As a Starfleet rank, it was used by the United Earth and Federation Starfleet.

On the 2140s-early 2160s Starfleet uniform, rear admirals, such as Daniel Leonard, were denoted by two rank insignia enclosed in a rectangular frame, worn on both sides of a uniform jacket. These officers also had a series of rank stripes on their sleeve, a group of four stripes (three in a group, and one separate towards the cuff). (ENT: "Broken Bow")

Later Starfleet rear admirals, such as James T. Kirk, were again denoted by sleeve stripes, this time signified by a similar insignia, one solid band of braid, and an additional stripe separate. Rear admiral's shoulder insignia, for epaulet uniforms, was a single eight pointed star. (Star Trek: The Motion Picture)

On the late 2270s-2350s Starfleet uniform, Kirk, and all other officers, wore their insignia as a pin device attached to the shoulder on the jacket clasp. The rear admiral pin was a small round field with four gold arrowheads arranged pointing towards the center, and was accompanied by an embroidered sleeve stripe. (Star Trek II: The Wrath of Khan)

In the 2360s, rear admirals like Starfleet Academy superintendent Brand, were denoted by two gold rank pips surrounded by a square frame. (TNG: "The First Duty")

Starfleet rear admirals

Background information

Robert Blackman's production notes during Star Trek: The Next Generation described this rank as "2 Starfleet Admiral, gold framed bar w/2 dots." [1](X)

The Star Trek Encyclopedia (3rd ed., p. 210-211) labeled this rank as "rear admiral" referring to the late 2270's-2350's uniforms, and "admiral, two star" referring to its use on 2350s-2370s, late 2360s-early 2370s, and 2370s uniforms.

Star Trek: The Magazine Volume 2, Issue 10, p. 99, mistakenly identified the late 2270's-2350's commodore insignia as the rear admiral insignia.

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