The phrase "a new insistence" is correct and usable in written English.
It can be used to describe a recent or renewed emphasis or demand for something.
Example: "The committee expressed a new insistence on the importance of sustainability in all future projects."
Alternatives: "a fresh demand" or "a renewed emphasis".
What changed last year, it says, was a new insistence on transparency.
There was a new insistence on the virtue of fidelity and on the sin of betrayal.
The current regime has turned its back on political reform, tightening internal security and promoting a new insistence on socialist dogma.
Some mining continues, new investment in lead, uranium, and even rubies, but there are now protest movements against some of these and a new insistence by Greenlanders for a different structure for employment, ownership, increased royalty, and profit-sharing.
His new insistence on a strict timetable is partly intended to burnish a nationalist image in the face of his populist Shia rival, Muqtada al-Sadr, who has long demanded the immediate removal of the Americans.
In some areas, including North Korea's new insistence on retaining a civilian nuclear power program and its firm denials that it has been developing fuel from enriched uranium, the gap appeared wider now than before the talks began.
Anyway, sitting on my back porch, I got a new idea: Insistence is resistance.
He is particularly effective in his critique of the court's new insistence that Congress justify its legislative choices by compiling an evidentiary record rather than relying on what the justices have belittled as mere anecdotes.
New insistence from Democrats on access to inexpensive drugs will be good for Teva, the Israeli generic drug manufacturer that fills one in every eight U.S. prescriptions.
In a more contemporary example, the entire plot of Mad Men is basically driven by white men railing against the new insistence of women, African-Americans, and homosexuals that they, too, should have meaningful work and be treated with respect.
In 2006, the original shark, having deteriorated, was replaced at Hirst's insistence by a new formaldehyde-injected one, which was then loaned to the Metropolitan Museum of Art in New York.
