The phrase "has been actively engaging" is correct and usable in written English.
You can use it to indicate that someone has been engaging in something in a consistent and purposeful manner over a sustained period of time. For example: "The organization has been actively engaging with local communities since its inception."
Hygiene-promotion sessions In Port-au-Prince, UNICEF has been actively engaged in community information activities related to cholera prevention, sanitation and medical response.
Twitter has been "actively engaged in cooperation," the statement said.
Since 1996, the community has been actively engaged in operations with mixed success to collect intelligence on bin Laden and disrupt his network.
Second, I can offer a perspective as someone who has been actively engaged in building and managing a national brand for 30 years.
When she has been actively engaged in the hand-to-hand combat that characterizes election campaigns and battles in Congress, her favorability ratings have taken a hit, only to recover later.
"They want someone to provide solutions to problems, and they are tired of the government getting too much in their business out there," said Nancy Keenan, a former state legislator in Montana who is now president of Naral Pro-Choice America, an abortion rights group that has been actively engaged in Western Congressional races.
Rishi Jain, the social inclusion officer for Liverpool who helped compile the guide, explained: "As part of the club's continued commitment to tackle all forms of discrimination, as well as promoting its approach to equality and diversity, Liverpool FC has been actively engaged in a full club-wide education and awareness programme.
Burkle pointed out that, unlike Dow Jones, the family that owns the New York Times has been actively engaged in managing the property.
