The phrase "are engaged in a contract" is correct and usable in written English.
You can use it when referring to parties that are currently involved in a contractual agreement.
Example: "The two companies are engaged in a contract to collaborate on the new project."
Alternatives: "are involved in a contract" or "are part of a contract".
CBS and Time Warner Cable have been engaged in a contract fight that has left millions of residents in cities like New York, Los Angeles and Dallas without access to the network's programming on their TVs and computers for almost a week.
The last time there was this much preseason pessimism was in 2007, when the left tackle and two linebackers were sent packing, the star defensive lineman was engaged in a contract holdout (Michael Strahan's was more conventional than Umenyiora's) and the acumen of the new general manager, Jerry Reese, was being questioned.
He may never look like some of the offensive line behemoths whose jerseys stretch so tightly over their torsos that they appear to be made of plastic wrap, but Ferguson's growing belly is good news for a young offensive line that may still lose guard Pete Kendall, who is engaged in a contract dispute with the Jets.
Private companies are engaged in an "arms race" to win NHS contracts.
Princeton wouldn't go online until the early 80s, but just up the road in Fresh Pond, Massachusetts, Bolt, Beranek & Newman, an engineering firm with a staff list heavy on ex-Princeton mathematicians was engaged in a U.S. military contract to build the Arpanet, the forerunner to today's web.
An automobile salesperson and a potential customer will be engaged in a cooperative game if they agree on a price and sign a contract.
Since February, the comptroller and the mayor have been engaged in a bitter dispute over all 17 welfare-to-work contracts.
The school board has been engaged in a long power struggle with Roberts, clashing over the signing of contracts for several unpaid board appointees.
Since then, Keegan has been engaged in a compensation dispute with Newcastle, with the club counter-claiming against him for not fulfilling his contract.
The company and its two main unions, one representing the orchestra and the other representing the chorus, singers and stage managers, are engaged in contract talks.
In developing countries, six in 10 young people are engaged in irregular employment: a salaried worker with a contract of less than a year, a self-employed young person with no employees and contributing family workers.
