(covers information from several alternate timelines)
This page contains information regarding Star Trek: Discovery, and thus may contain spoilers.
Parking could refer both to the act of leaving behind a vehicle at a certain spot, and to specific locations designated for parking, which might also be called a parking lot. The term was most often used in relation to cars and other ground vehicles, but it could also apply to spaceships capable of landing.
On 20th century Earth, there were sometimes restrictions on parking, or even personel tasked with coordinating parking. Once while in 1996, Tuvok unsuccessfully tried to use Vulcan logic to talk a meter maid out of giving him a citation. The homeless Braxton had set up in an alley where no parking was allowed, as indicated by a sign. Inexplicably the alley contained a derelict automobile regardless. (VOY: "Future's End")
In that same year, signs directing cars to a parking space could be found near the Sentinel building in San Francisco. A nearby antiques shop also had a sign saying "Don't even think of parking here" on sale. (Star Trek IV: The Voyage Home)
Starships might also assume a parking orbit, or otherwise be parked at a specific location in space. Ro Laren for example once docked a ship between two warp nacelles. (TNG: "Preemptive Strike"). Starships might incorporate a parking brake. (Star Trek)