Singer of half poor parts, possibly? (3,4)
I believe the answer is:
pop star
'singer' is the definition.
(I have seen 'Popular singer ' mean 'pop star' so perhaps 'singer' could also mean 'pop star')
'half poor parts possibly?' is the wordplay.
'half' suggests halving the letters.
'possibly?' is an anagram indicator (I've seen 'possibly' mean this).
'poor' with half the letters taken is 'po'.
'parts' is an anagram of 'pstar'.
'po'+'pstar'='POP-STAR'
'of' acts as a link.
(Other definitions for pop star that I've seen before include "Chart musician" , "Musical celebrity" , "Popular singer" .)