Ostentatiously good, a female performer with no regrets (4)
I believe the answer is:
piaf
'performer with no regrets' is the definition.
I can't judge whether this definition defines the answer.
'ostentatiously good a female' is the wordplay.
'ostentatiously good' becomes 'pi' (old-fashioned term for pious).
'female' becomes 'f' (common abbreviation).
'pi'+'a'+'f'='PIAF'
Can you help me to learn more?
(Other definitions for piaf that I've seen before include "Edith -, twentieth century French cabaret singer" , "Edith -, Fr. cabaret singer (Non, je ne regrette rien)" , "See 6 Down" , "Edith, the "Little Sparrow"" , "French singer, the Little Sparrow, d. 1963" .)