Very gradually start off to conceal excavation (9)
I believe the answer is:
eminently
'very' is the definition.
(thesaurus)
'gradually start off to conceal excavation' is the wordplay.
'gradually' becomes 'gently' (I've seen this before).
'start off' means to remove the first letter (I've seen 'starting off' mean this (the starting letter is removed)).
'to conceal' indicates putting letters inside.
'excavation' becomes 'mine' (mine is a kind of excavation).
'gently' with its first letter taken off is 'ently'.
'ently' enclosing 'mine' is 'EMINENTLY'.
(Other definitions for eminently that I've seen before include "In an outstanding manner" , "well" , "to a notable extent" .)