"premier establishment" is a correct and usable phrase in written English.
It can be used to describe a business or organization that is considered to be of the highest quality or status in its field. Example sentence: The new luxury hotel in the city is quickly gaining a reputation as the premier establishment for top-notch accommodations and service.
In one of the novel's more poignant moments, Sepha and Joe stare at one another through the vast plate-glass windows that envelop the Colonial Grill, "the premier eating establishment of the District's elite".
Along with Cambridge, Oxford University is the premier educational establishment in the UK.
It was undermined, however, by church interests, which were opposed to its lack of ecclesiastical control, and criticism of the efficiency of its management, hence losing much of its earlier prestige as the premier educational establishment in the town.
Given Carnegie's new partnerships with organizations such as the Google Culture Institute and the launch of major new projects like its digital archives, webcasting of concerts to audiences around the globe, and the National Youth Orchestra of the United States of America, it will continue as the world's premier musical establishment.
If the wall of candles is reminiscent of the Besito restaurants in Huntington and Roslyn, the island's premier Mexican establishments, it's not a coincidence.
The present paper provides a brief description of the biomedical waste (Management and Handling) Rules 1998, and the current biomedical waste management practices in one of the premier healthcare establishments of Lucknow, the Vivekananda Polyclinic.
While you're here, you must visit the Criterion Restaurant, regarded as one of London's premier fine dining establishments, it's utterly soaked with history.
Earlier in 2008, Senator Charles Grassley (R-Iowa) was particular troubled by what investigators told him about psychiatry's premier professional organization, the American Psychiatric Association (APA), described by the New York Times as "the voice of establishment psychiatry".
Less than two decades after Murdoch's money funded the establishment of the Premier League, the top tier of English football presents a gruesome spectacle in which clubs who should be leading prosperous existences find themselves lured by financial promiscuity to the brink of disaster.
The influx of foreign players, part of what the man who hosted the dinner in the early 90s that led to the establishment of the Premier League called "the law of unintended consequences", is now acting as a blockage of the development of players for England's national side.
