(covers information from several alternate timelines)
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A tracking device was an object that permitted the changing location of vehicles and individuals to be determined and monitored.
After travelling from the 23rd century to 1986 San Francisco, Spock cautioned James T. Kirk that the HMS Bounty would likely be detected by the tracking devices of the 20th century. Kirk concurred and ordered Pavel Chekov to engage the Bounty's cloaking device. (Star Trek IV: The Voyage Home)
In 2263, after learning that Spock had given Nyota Uhura an amulet made out of vokaya, Leonard McCoy expressed surprise over the fact that Spock had given his girlfriend what was essentially a tracking device, something that Spock assured the doctor was not his intention. (Star Trek Beyond)