Training establishment with shaky foundation damaged — start to search inside (9)
I believe the answer is:
sandhurst
'training establishment' is the definition.
(Sandhurst is a military training base)
'with shaky foundation damaged start to search inside' is the wordplay.
'with' says to put letters next to each other.
'shaky foundation' becomes 'sand' (as in something built on sand).
'damaged' becomes 'hurt' (similar in meaning).
'start to' indicates taking the first letters.
'inside' indicates putting letters inside.
The first letter of 'search' is 's'.
'hurt' enclosing 's' is 'hurst'.
'sand' put next to 'hurst' is 'SANDHURST'.
(Other definitions for sandhurst that I've seen before include "Training college" , "Seat of the Royal Military Academy" , "Village in Berkshire - military academy" , "Military college at Camberley, Surrey" .)