Famous English pit theatre (7)
I believe the answer is:
eminent
'famous' is the definition.
(I've seen this before)
'english pit theatre' is the wordplay.
'english' becomes 'E' (abbreviation).
'pit' becomes 'mine' (mining pit).
'theatre' becomes 'nt' (National Theatre).
'e'+'mine'+'nt'='EMINENT'
(Other definitions for eminent that I've seen before include "Noted" , "Exalted in rank" , "Distinguished, prominent" , "Respected; distinguished" , "Famous and respected" .)