CONSENT = ALLOW = ACQUIESCE = ACCEDE >< OBJECT = REFUSE = OPPOSE

(verb) to allow someone to do something: "She consented to a police search."
Synonyms
allow: "The seller allowed the buyer to make late payment."
acquiesce: "The court acquiesced to the defendant's request for an extension of time."
accede: "All of the countries at the conference acceded to the treaty."
Antonyms
object: "I object to the introduction of evidence of my client's prior crimes."
refuse: "The seller refused to allow the buyer to make late payment."
oppose: "He opposed any change to the terms and conditions of the agreement."

Related word
Assent is close in meaning, but implies a more active, voluntary and enthusiastic agreement, than consent, which can be reluctant. "The President gave her assent last week to a bill to impose stricter environmental standards on oil refineries."

Common phrases
"The landlord refused to consent to an extension of the lease."
"The seller consented to the buyer's request to delay payment."
"A patient must consent to medical treatment."
"The company consented to the use of their name on the website."
Source: Your Dictionary