"actively look for" is correct and usable in written English. You can use it when you are talking about actively searching or seeking out something. For example, "I am actively looking for a new job in my field of study.".
"We don't actively look for this stuff," Lieutenant Traina said.
Some of them will actively look for opportunities to murder.
We should actively look for ways to amplify women and girls' priorities and solutions for development.
They said that excellent companies actively look for excuses to hand out rewards.
Now they're actively looking for options".
They're actively looking for something downtown.
He was actively looking for a job elsewhere.
Thanks to Ludwig my first paper got accepted! The editor wrote me that my manuscript was well-written
Listya Utami K.
PhD Student in Biology, Bandung Institute of Technology, Indonesia