A provisional officer is an individual in a service organization who is given a promotion in rank or title to occupy an officer (or non-commissioned officer) position on a limited basis.
Promotions in title are often important to maintain a chain of command, and are granted at the discretion of a senior officer. For example, in the Kelvin timeline, Starfleet Captain Richard Robau named Lieutenant Commander George Kirk as commanding officer of the USS Kelvin when Robau surrendered himself to Nero in 2233. Likewise, Christopher Pike made a similar move, naming Spock as acting captain in his absence. In order to complete the chain of command, Pike also named Lieutenant James T. Kirk as acting first officer. (TOS movie & novelization: Star Trek)
Promotions in rank on a temporary basis may also be dispensed by an officer senior to the position in question. In 2364, Starfleet Captain Jean-Luc Picard named Wesley Crusher an acting ensign, and gave him a full field promotion to ensign in 2366. Also in 2366, Vice Admiral J.P. Hanson gave Commander William Riker an immediate field promotion to captain, and in turn, Lieutenant Commander Elizabeth Shelby was field promoted to commander to occupy the USS Enterprise-D's then-vacant first officer position. Shelby's promotion was later confirmed and became her permanent rank, although Riker declined his rank and resumed his role as a commander upon the return of Picard to the Enterprise crew. (TNG episodes: "Where No One Has Gone Before", "Ménage à Troi", "The Best of Both Worlds")
In a special case, Captain Kathryn Janeway gave provisional Starfleet officer and noncommissioned officer positions to the entire surviving crew of the Maquis raider under Chakotay's command in order to have them join her crew, and take part in USS Voyager's command structure. Chakotay was made a lieutenant commander and her first officer, resuming his former Starfleet career, and B'Elanna Torres became a lieutenant junior grade, resuming a career she left off as a third-year cadet at Starfleet Academy. Most of the rest of Chakotay's crew also became junior lieutenants, ensigns or noncommissioned officers and crewpeople, with special insignia to show their provisional. At the same time, former Starfleet officer Tom Paris was reactivated to his former Starfleet rank by Janeway after joining the crew. (VOY episode: "Caretaker")