The phrase "a joint exercise with" is correct and usable in written English.
It can be used to describe a collaborative activity or operation involving two or more parties or organizations.
Example: "The military conducted a joint exercise with allied forces to enhance their strategic coordination."
Alternatives: "a collaborative effort with" or "a cooperative activity with".
The best way to do this is a joint exercise with the Met police.
Britain has already sent four vessels as part of Operation Sophia and in a joint exercise with Nato to monitor the waters off Libya.
He told The Independent: "Last Thursday, on their normal training evening, the crew at Abersoch agreed to carry out a joint exercise with Bear.
Internationally, the Guardian Foundation this year supported a study group visit from Georgian journalists, and a joint exercise with the Slovenian Mirovni Institute to promote media plurality and freedom in the Balkans.
Then, after we made a few more phone calls, hundreds of U.S. marines -- marines! -- who were conducting a joint exercise with the Jordanian Army cut short their operation, got back on their amphibious vessels and fled Jordan on Saturday.
Those concerns seemed to gain impetus on Tuesday when Japan's army announced that a joint exercise with the United States Army that had been scheduled for next week in Japan had been canceled because of the shutdown.
Three times, he raised complaints about recent American naval maneuvers in or near the South China Sea, including a joint exercise this week with the Australian and Japanese Navies and a late June exercise with the navy of the Philippines.
On returning to the United Kingdom, he arranged for a joint exercise to be conducted with the 2nd Battalion, US 503rd Parachute Infantry.
Two ballistic-missile ships, which carry powerful tracking radars and interceptor missiles, had been in the area for a recent joint exercise with the South Korean military, but they had returned to Japan after that exercise ended.
The same day, the Israeli military announced that its air force had just completed a weeklong joint exercise with Italy's air force in Sardinia, practicing for operational capabilities in conditions that do not exist in Israel.
In late February, the United States was moving military forces into the region for an annual joint exercise with the South code-named "Foal Eagle." South Korea had canceled the 2018 exercise to avoid upsetting the North before the Winter Olympics in PyeongChang.
