For example, entreat nurses to continue without a break (5)
I believe the answer is:
segue
'continue without a break' is the definition.
(I've seen this in another clue)
'for example entreat nurses' is the wordplay.
'for example' becomes 'e.g.' (short for 'exempli gratia', 'for example' in Latin).
'entreat' becomes 'sue' (I've seen this before).
'nurses' means one lot of letters goes inside another (nurse can mean to hold onto or harbour).
'eg' put into 'sue' is 'SEGUE'.
'to' is the link.
(Other definitions for segue that I've seen before include "carry on" , "In music, an immediate transition from one part to another" , "Keep going without interruption" , "Proceed immediately" , "Change smoothly from one thing to another" .)