The rank of grand admiral or grand-admiral was a grade of admiral in a naval service organization that was equivalent to or outranking of a fleet admiral. The flag officer rank of grand admiral was used by service organizations, including in the 23rd century by senior staff at the highest levels of the Federation Starfleet.
His service uniform appeared to be essentially standard for a Starfleet flag officer, but his formal uniform as Starfleet grand admiral was markedly different from the uniforms worn by other Starfleet officers. The maroon officer's tunic had two shoulder tabs ornamented with rank insignia and both wrist cuffs adorned with unique braid. Optional uniform accessories included an undershirt with ornamented collar, a white sash, and award ribbons worn above the brass Starfleet insignia. (TOS comic: "The Wormhole Connection")
By the 24th century, Pavel Chekov had reached the rank of grand admiral, and was considered the foremost authority of Starfleet. In 2375, Jean-Luc Picard felt very strongly in his opposition to Starfleet orders to allow the Ferengi to donate sensor technology to the planet Halkan—so much so, in fact, as to feel that he would disobey even Chekov's orders, if they had indeed been the orders that put him at odds with Captain Christine MacDonald in that situation. (TOS novel: Preserver)
Terran Empire Starfleet
In the Terran Empire's mirror universe Starfleet, grand admiral was one of the many ranks available to those who excelled in the brutal power plays of the Imperial control of the galaxy in the 23rd century. 
Imperial Klingon States
Orion rebel forces
Finit the Iron-Handed was a Grand-Admiral of the massed Orion fleets at the Battle of Rhinate in December, 57 BCE (reference stardate −20/5712). (FASA RPG - The Orions module: Book of Common Knowledge)
- As the Orion fleets at the time were former pirates turned to guerilla warfare in rebellion, it seems likely that "Grand-Admiral" is not an official or standard rank. It does not appear in the Orion Space Navy that later developed.
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This rank was originally created for Star Trek use by William Rotsler in his book Star Trek II Biographies as a means of having someone who outranked an admiral. Mike W. Barr used it (and the character of Stephen Turner) in the first several issues of the first comic book series published by DC Comics. After a mention in Preserver, the rank was never heard from again in Federation settings, although some other Star Trek stories mention it being used by the Klingons, Tholians, and the Terran Empire.
The United States rank scheme that Starfleet was adapted from lacks a "grand admiral" rank, although there were European naval services that used this rank on Earth at various times, most notably Germany, where it was usually approximately equivalent or superior to the "five star" fleet admiral grade. The closest grade to this high rank that the United States Navy has established was a one-time Admiral of the Navy grade. The only actual US naval insignia ever used for a rank above fleet admiral was created for Admiral of the Navy: four silver stars framed by two gold anchors as pin insignia, and a single half-inch gold stripe between two two-inch gold stripes as sleeve insignia.