Weak person bleeds before surgery (7)
I believe the answer is:
milksop
'weak person' is the definition.
(milksop can mean a cowardly person)
'bleeds before surgery' is the wordplay.
'bleeds' becomes 'milks' (milk can mean to bleed or exploit).
'before' says to put letters next to each other.
'surgery' becomes 'op' (short for operation).
'milks'+'op'='MILKSOP'
(Other definitions for milksop that I've seen before include "Chinless wonder" , "Feeble ineffectual man" , "Cissy (informal) -- limps OK (anag)" , "Wimpish fellow" , "Weed" .)