(covers information from several alternate timelines)
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The Starfleet promotion ceremony took place when a Starfleet officer was promoted to a higher rank. The ceremony involved pinning the pip of the new rank on the officer's collar by their commanding officer or equivalent thereof. (VOY: "Revulsion")
In 2258, James T. Kirk was promoted to captain of the USS Enterprise by the Starfleet Academy Board, for saving Earth from Nero. Admiral Richard Barnett pinned a medal to Kirk's dress uniform to signify his new rank. (Star Trek)
Also in 2371, the senior staff of the USS Enterprise-D used a ceremony incorporated into an elaborate holodeck recreation of a 19th century sailing ship, for Lieutenant Worf's promotion to lieutenant commander. (Star Trek Generations)
In 2374, on stardate 51186.2, Lieutenant Tuvok was promoted to lieutenant commander on board the USS Voyager during a promotion ceremony presided over by Captain Kathryn Janeway in Voyager's mess hall. (VOY: "Revulsion")
In 2377, Tom Paris was promoted back to lieutenant junior grade following a previous demotion to ensign. The ceremony took place when he started his duty shift to find a box containing his new pip at his station. (VOY: "Unimatrix Zero")