The phrase "agrees to engage" is correct and usable in written English.
It can be used in contexts where someone is committing to participate or take part in an activity or agreement.
Example: "The company agrees to engage in negotiations with the union to discuss the new contract terms."
Alternatives: "commits to participate" or "consents to take part".
"I am hopeful we can resolve the shutdown as soon as the Senate agrees to engage in a conversation.
South Korea agrees to engage in talks with North Korea over the future of a joint industrial complex in Kaesong, N.Kor.
But if the Russians make it clear that they will stop arming Syrian government forces, withdraw their technicians and lift their diplomatic cover at the United Nations, unless Damascus agrees to engage in serious discussions with the opposition, the Kremlin will not be ignored.
The work with the multidisciplinary team can only be carried out if the child agrees to engage in the conception of his assistive technology by means of PD4CAT.
This week, he graciously agreed to engage in The Exchange.
Then, suddenly, Nkunda called off his advance, and agreed to engage in negotiations with the government.
Parties agreed to engage in settlement negotiations, and to submit their class action settlement proposal to Judge Koh for approval.
Mr. Rouhani has agreed to engage in talks with the United States and other Western powers over Iran's nuclear program, which he insists is solely for civilian purposes.
They agree to engage in a storytelling contest as they travel, and Harry Bailly, host of the Tabard, serves as master of ceremonies for the contest.
By agreeing to engage in deal design jointly, the Republicans made it much more difficult for their future negotiating counterparts to ignore their demands.
"We agree to engage in vigorous, ongoing and continuous negotiations, and shall make every effort to conclude an agreement before the end of 2008".
