The phrase "under directions from" is correct and can be used in written English.
It is used to indicate that someone or something has received orders from someone else. For example, "The students completed the project under directions from their professor."
While publishing more contracts and detailed expenditure is progressive, benchmarking reports can only be published under direction from the mayor.
The Big Lottery Fund currently distributes money that is charitable, connected with health, education or the environment, under direction from the Government.
The British plot was thwarted in October 2014 and involved Tarik Hassane and at least one other young man from west London, under direction from overseas.
What's different is that under direction from Governor Whitman, state agencies have begun to use the plan to guide their regulations and spending.
At present the foreign minister can cancel passports – and has pulled about 12 – but only at the request of police under direction from state governments.
More and more goods are now made in the poor countries of the southern periphery under direction from headquarters in the north and most are destined to be consumed in the industrial heartland.
It has given 426 residents high-performance vacuum cleaners and, under direction from the E.P.A. and the Missouri Natural Resources Department, is systematically replacing contaminated soil in the town's 535 parcels.
Time Inc. is under direction from AOL Time Warner's management to increase the magazine division's revenue, and executives at Time Inc. said that there would be an effort to increase Golf magazine's circulation.
"This whole situation could have been avoided if London Underground, under direction from the Mayor, had dealt with the night Tube professionally from the off instead of resorting to ultimatums and imposition.
