es‧tab‧lished W3 [only before noun]
already in use or existing for a long period of time:
Competition from established businesses can be formidable.
well-established teaching methods
By 1969 the civil rights movement was already an established fact.
Every once in a while, the established order (=people who rule) is overthrown.
known to do a particular job well, because you have done it for a long time:
an established professor of French literature
3 especially British English
the official church or religion in a particular country