Classified, privileged, or top secret information was confidential material with restricted access. Information that was suppressed could be considered a cover-up.
In 1996, time traveler Tuvok from 2373 responded to Rain Robinson's question about his and fellow time traveler Tom Paris' weapons (phasers) by stating that the information was classified. Robinson later asked Paris what life as a spy was like but he said it was classified. (VOY: "Future's End")
A file titled Talos IV was classified as top secret, and only intended for reading by officers of Starfleet Command. (TOS: "The Menagerie, Part I")
In 2257, the personnel file of Captain Christopher Pike was classified. Pike was also briefed on the classified details surrounding the USS Discovery's previous captain, Gabriel Lorca. (DIS: "Brother")
In 2364, a holographic Paul Rice stated that the location of the USS Drake was classified. (TNG: "The Arsenal of Freedom")
In 2373, Captain Kathryn Janeway examined the Starfleet database for classified information on the Borg. (VOY: "Scorpion")
Starfleet Command classified all knowledge of Omega molecules as a military secret of the highest order and enacted the Omega Directive, on which only starship captains and flag officers were briefed. (VOY: "The Omega Directive")
In 2378, Tuvok suggested claiming that the holonovel Photons Be Free revealed classified information so that Starfleet could request that the holonovel be recalled for security purposes. (VOY: "Author, Author")
When Kovich assisted Doctor Hugh Culber into his research for a cure for Philippa Georgiou's unique condition, he activated classified file Beta-4895-Omega, which contained information about Yor, a time soldier who was the only other individual known to have travelled through time, and across dimensions. (DIS: "Terra Firma, Part 1")