The phrase "accepted a request" is correct and usable in written English.
It can be used when indicating that someone has agreed to or acknowledged a request made by another person.
Example: "After reviewing the proposal, she accepted a request to collaborate on the project."
Alternatives: "agreed to a request" or "acknowledged a request".
"The club initially accepted a request from the PFA for Ched Evans to be able to train.
He then denied a defense motion for a mistrial and accepted a request from the jurors to break for the weekend.
Ultimately, she wound up talking to an executive who had just accepted a request for a sabbatical from a high-level employee.
Dimon has accepted a request from senator Tim Johnson, chairman of the committee, who said it should "hear directly" from Dimon about the losses at America's biggest bank.
On May 30th, American officials accepted a request from Russia, Iraq's closest ally among the permanent members of the UN Security Council, to postpone a vote on their new resolution.
On March 10 the InterAcademy Council (IAC), which represents national science academies, accepted a request by the UN and the IPCC to appoint a panel to investigate the IPCC's procedures.
After denying a defense motion for a mistrial, the judge accepts a request from the jurors to break for the weekend.
It is possible that the United States Supreme Court would then accept a request from Governor Bush to take up the case a second time.
In Brazil, the Sarney case is just the latest example of a lower court's accepting a request to prevent a media outlet from broadcasting or publishing reports on suspected corruption.
And one says limousines may not accept a request for a ride that is made less than 30 minutes in advance, which would impede Uber's primary business model of connecting luxury car drivers with passengers immediately.
I have distinct memories of standing in the post office filling out registered mail forms since that was the only way some of the companies would accept a request to freeze a file.
