Secret pub Metro 's written about (9)
I believe the answer is:
innermost
'secret' is the definition.
(as in one's innermost thoughts)
'pub metro 's written about' is the wordplay.
'pub' becomes 'inn' (an inn is a type of pub).
'written about' indicates anagramming the letters (letters moved about before being rewritten).
'metro'+'s'='metros'
'metros' anagrammed gives 'ermost'.
'inn'+'ermost'='INNERMOST'
(Other definitions for innermost that I've seen before include "Private" , "Sort of secrets" , "Who may have gone deepest" , "farthest from border" , "Furthest in" .)