The phrase "make a plea" is correct and can be used in written English.
You can use it when describing an act of pleading guilty or not guilty in a court of law. Example: The defendant made a plea of not guilty.
They make a plea for social justice.
"You can't make a plea deal while arrested.
"I went to see Sir Keith Joseph [then education secretary] to make a plea for clemency.
She refused to make a plea bargain, choosing instead to go to trial.
If anything, the issue could intensify should Conte make a plea arrangement with the prosecutors.
But if prosecutors make a plea offer, the court now requires that defendants have effective counsel in considering the offer.
She also risked an ugly trial and a longer prison sentence if she did not make a plea deal.
But I'm going to make a plea for julienning them, either by hand or with a mandoline.
In that case, Lieberman said, he would "make a plea" to his colleagues on Petraeus's behalf to defeat it.
The Pres. had been scheduled to make a plea to Congress for early enactment of pending civil-rights legislation.
