Feel concern or interest (4)
I believe the answer is:
care
I believe this clue is a double definition.
'feel concern' is the first definition.
(synonyms)
'interest' is the second definition.
(thesaurus)
(Other definitions for care that I've seen before include "Caution, regard for safety" , "Protective custody" , "Race (anag.)" , "Worry" , "Be concerned or nurse" .)