Contralto possibly - but hard to please! (5,5)
I believe the answer is:
prima donna
'contralto' is the definition.
(thesaurus)
'but hard to please' is the wordplay.
I cannot quite understand how this works, but
'please' could be 'do' (I've seen this in other clues) and 'do' is present in the answer.
This explanation may well be incorrect...
'possibly' acts as a link.
Can you help me to learn more?
(Other definitions for prima donna that I've seen before include "Top female singer" , "Very self-important person" , "Female opera star" , "Leading lady, proverbially temperamental" , "lady centre stage" .)