The phrase "an established interest" is correct and usable in written English.
It can be used to refer to a recognized or acknowledged area of concern or focus, often in contexts like finance, research, or personal interests.
Example: "The organization has an established interest in environmental sustainability and actively supports related initiatives."
Alternatives: "a recognized interest" or "a well-defined interest".
"For instance, I would have assumed there was now an established interest in working-class women's history.
Dr. Richter has an established interest in healthcare systems development and quality management, infectious, and inflammatory enteric diseases.
This study examined sports medicine physicians with an established interest in physical activity to investigate attitudes surrounding exercise, physical activity and patient-counseling behavior.
They came from rural and suburban towns in Northeastern states, many with an established interest in the outdoors, and some drawn, paradoxically, by lumberjack competitions they had seen on television.
The California attorney general said that the law did not inhibit free speech, but rather regulated the conduct of licensed professionals, and that the government had an established interest in barring practices deemed ineffective or potentially harmful.
Imagine a coalition of major community foundations coming forward, along with the major foundations with an established interest in disadvantaged children and education (Gates, Broad, Annie E. Casey) to support a national pre-K movement.
So it has a well established interest in pushing the envelop on video game content — say by being able to offer gamers photorealistic avatars.
There is a strong and long established interest in diseases of the gastrointestinal tract, liver, biliary tract, and pancreas at Yale, with outstanding research programs in each area.
More, the complexity benefited a number of established interests.
It is situated in an area where the established interests of the great powers are pitted against those of rising regional powers, against the backdrop of a reemergence of blind religious fundamentalism, in the form of the Islamic State -- a serious menace to universal human rights and a threat to the principles and values of rationalism.
The equivalent for Internet entrepreneurs is a rhetoric of fighting established interests on behalf of ordinary people.
