Care for those experiencing niggling delays at first (4)
I believe the answer is:
tend
'care for' is the definition.
(thesaurus)
'those experiencing niggling delays at first' is the wordplay.
'at first' suggests taking the first letters.
The first letters of 'those experiencing niggling delays' is 'TEND'.
(Other definitions for tend that I've seen before include "Go in a particular direction; look after" , "Incline; cultivate" , "Care for, nurse" , "Have leaning towards - put dent in (4)" , "Wait on" .)