Problem, not the first, to make one worry (3)
I believe the answer is:
nag
'one worry' is the definition.
(thesaurus)
'problem not the first' is the wordplay.
'problem' becomes 'snag' (I've seen this before).
'not the first' means to remove the first letter.
'snag' with its first letter removed is 'NAG'.
'to make' acts as a link.
(Other definitions for nag that I've seen before include "Badger continually like old horse" , "Annoy the old horse persistently" , "Henpeck like old horse" , "Find fault" , "Henpeck, scold non-stop" .)