Butcher's pursuing nurse (4,5)
I believe the answer is:
look after
'nurse' is the definition.
(I've seen this before)
'butcher's pursuing' is the wordplay.
'butcher's' becomes 'look' (I've seen this in other clues).
'pursuing' becomes 'after' (if you're pursuing something you're after it).
'look'+'after'='LOOK AFTER'
(Other definitions for look after that I've seen before include "Tend" , "nurse" , "Supervise" , "Peer trying to find" , "Take care of" .)