(covers information from several alternate timelines)
Consent, or permission, was the act of permitting an individual to do something.
In 2254, Lieutenant Commander Una Chin-Riley asked for permission from Captain Christopher Pike for sending scouting and scientific parties to the surface of Talos IV. Pike gave his consent, saying "Affirmative on the request". (TOS: "The Cage")
In 2366 in an alternate timeline in which the United Federation of Planets was in a war with the Klingon Empire, Captain Jean-Luc Picard gave the order to send the USS Enterprise-C back through a temporal rift in the hopes that their attempt to save a Romulan outpost might prevent the war before it even started. Commander William T. Riker started to offer his opinion on this, but Picard cut him off, saying that he was aware of his opinion, but it was a briefing and he wasn't seeking his consent. (TNG: "Yesterday's Enterprise")
In the 31st century, feeling the new technology might be too dangerous, scientists requested permission from the Federation to shutter the experimental program SB-19. The Federation, believing the program offered the best alternative to their current dilithium crisis, replied in the negative. (DIS: "Unification III")
In 3189, President T'Rina initially denied a request for data related to SB-19 from the Federation. Later, T'Rina reversed the decision, believing that trusting Commander Michael Burnham, the Federation representative, was worth the risk. (DIS: "Unification III")