The phrase "already a priority" is correct and usable in written English.
You can use it to indicate that something has been designated as important or urgent prior to the current moment or discussion.
Example: "The safety of our employees is already a priority for our management team."
Alternatives: "has been prioritized" or "is a top concern".
Gender was already a priority for DfID before the passage of the act, the report said.
Contacted on Wednesday, Fertility Solutions PGD said in a written message that the surrogates and families were "already a priority so no need to report on it".
Reducing the cost of bids was already a priority for IOC president Thomas Bach, and now we can see why.
The Times says the intervention has angered Tory MPs, who say health spending is already a priority and accuse the group of "scaremongering".
The fact here is that Mars is already a priority and they have major missions planned already, but to say anything about a crewed mission or base would be irresponsible and premature.
These are problems that are tied to climate change, but are already a priority on the local level.
Although Connecticut already has a priority list for barriers for noise abatement, Mr. Maloney said safety has to take priority over sound.
His title is a new one at G.M., but the company had begun recruiting him months before Sept. 11, an indication that information security had already become a priority for senior management.
And the Police Department has already made a priority of enforcing speed: Officers have issued about 95,000 speeding summonses so far this year, compared with 69,000 in the same period last year.
Mejía was eager to point out that although the decision to confront the Vat's physical and structural problems came just after his departure, certain aspects of the modernization — the decision to use computer tagging for the printed books, for instance — had already become a priority when he arrived.
Telecommunications giant AT&T in June took over Time Warner, HBO's longtime parent, and the new management signaled that it wants HBO to increase its output, which had already been a priority for HBO's management.
