"new cooperation" is a correct and usable phrase in written English.
You can use it when referring to a collaboration or alliance that has either just begun or been recently formed. For example: "The two companies are hoping that their new cooperation will help them meet their financial goals."
Eyes on the South Media Advisory UNICEF and Hungary sign new cooperation agreement New York, 14 December 2007 – Hungary has become the first of the twelve new EU members to sign a Framework Agreement on Cooperation in... UNICEF condemns continuing violence in Mount Elgon NAIROBI, 14 December 2007 Todayay UNICEF condemned continuing attacks on families in Mount Elgon District.
Additional US$45 million contribution to Syria's children, as EU becomes largest donor to UNICEF appeal NEW YORK, 24 September 2013 – UNICEF and the European Union (EU) signed a new cooperation agreement today that provides an additional US$45 million (€34. 22 million) to protect children affected by the Syria crisis and promote access to learning in Syria, Jordan and Lebanon.
NEW YORK, 24 September 2013 – UNICEF and the European Union (EU) signed a new cooperation agreement today that provides an additional US$45 million (€34. 22 million) to protect children affected by the Syria crisis and promote access to learning in Syria, Jordan and Lebanon.
That has raised administration hopes of new cooperation.
There are also signs of new cooperation on Syria.
Both governments took care to say that their new cooperation was not intended to isolate Germany.
Still, some officials see the new cooperation between the West and Belgrade over Presevo as promising.
"And I believe the new cooperation will continue to yield new outcomes".
Officials said it reflected a new cooperation between the C.I.A. and the military.
At China's embassies in the region, diplomats are open to talk of new cooperation.
In exchange, the foreign ministers of Britain, France and Germany promised new "cooperation" -- meaning trade -- in high technology with Tehran.
