Health problem — is it sore throat possibly? (14)
I believe the answer is:
osteoarthritis
'health problem' is the definition.
(osteoarthritis is a kind of health problem)
'is it sore throat possibly?' is the wordplay.
'possibly?' indicates an anagram (I've seen 'possibly' mean this).
'is'+'it'+'sore'+'throat'='isitsorethroat'
'isitsorethroat' is an anagram of 'OSTEOARTHRITIS'.
(Other definitions for osteoarthritis that I've seen before include "something a specialist should handle?" , "degenerative condition" .)