"well-established reputation" is correct and usable in written English.
You can use it to describe a business, individual, or organization that has a long-standing well-respected history. For example, "This company holds a well-established reputation in the industry for providing excellent customer service."
Florida has a well-established reputation as a swing state.
This is particularly true for newer universities, who may not have a well-established reputation".
Diving: Dive Dominica, (888) 414-7626 and www.divedominica.com, has a well-established reputation and is convenient.
The respondent, Claude Théberge, is a painter who enjoys a well-established reputation in Canada, the United States and Europe.
Accustomed to being fawned over by foreign leaders, Modi will find himself being confronted by a man with a well-established reputation for moral authority.
This highly satirical strip attempts to poke fun at the Director and the Bureau's well-established reputation for loyalty, patriotism and high moral behavior.
Without Lin and Stoudemire, the offense shifts toward Anthony, Davis and J. R. Smith, three veterans with well-established reputations as high-usage, low-efficiency scorers.
A French victory in Nice seems out of the question considering the strengths, polish and well-established reputations of Davis and White, and of Virtue and Moir.
These men had little to gain personally by their investigations; indeed in undertaking them they endangered already well-established reputations.
He is one of a handful of international scholars with well-established reputations as authorities on Leonardo whose backing the foundation would ideally like to secure.
In places like Brazil, which scored 3.7 on Transparency International's 2009 Corruption Perceptions Index (where 10 represents the total absence of corruption), GE recorded $2.5 billion in 2009 revenues and likely faced far fewer bribery demands than others with less well-established reputations for probity.
