Second nag is a non-starter (5)
I believe the answer is:
other
'second' is the definition.
(I've seen this before)
'nag is a non-starter' is the wordplay.
'nag' becomes 'bother'.
'is a non-starter' means to remove the first letter (the letter which starts the word is removed).
'bother' with its first letter taken off is 'OTHER'.
(Other definitions for other that I've seen before include "Alternative of two" , "Different (from those mentioned)" , "Different; additional" , "Different, alternative" , "Alternative - unrelated" .)