Compete with prisoner and nurse (7)
I believe the answer is:
contend
'compete with' is the definition.
(thesaurus)
'prisoner and nurse' is the wordplay.
'prisoner' becomes 'con' (abbreviation for 'convict').
'and' says to put letters next to each other.
'nurse' becomes 'tend' (tend can mean to nurse or look after).
'con'+'tend'='CONTEND'
(Other definitions for contend that I've seen before include "Tend NCO (anag.)" , "Debate - contest - claim" , "Maintain" , "Compete, vie" , "Engage in a struggle" .)