"consistently seeking" is a correct and usable phrase in written English.
It means to actively and continuously search for something or someone. Example: Sarah is consistently seeking ways to improve her skills and knowledge in her field of work.
Customers, clients as well as employees are consistently seeking out organizations that have transparency and show social responsibility.
The Lizard Brain: Our "Lizard Brain" is the part of our brain that is most impulsive and consistently seeking basic essentials for life: eat food, reproduce, stay safe.
In a statement, the Sun-Times said, "The Sun-Times business is changing rapidly and our audiences are consistently seeking more video content with their news.
Consistently seeking feedback and being transparent about any company changes will boost employee productivity and make the workplace a lot more enjoyable.
Refusing to offer help to others and consistently seeking one's own good and disregarding the good of others will result in one's being denied the help and goodwill that may be necessary to achieve certain ends.
The league has thrived off of its progressive approach to its business model; consistently seeking to innovate the way the sport is consumed and experienced.
We consistently seek to implement world class manufacturing techniques.
Elephants consistently seek out greener than expected vegetation throughout the year.
Ending his exile was something Berezovsky consistently sought, said another journalist and acquaintance, Mikhail Kozyrev.
Mr. Holzer said that "the museum has consistently sought and received government approvals".
The government has consistently sought to block Belhaj from bringing a case against it.
