Feeble daughter about to languish (5)
I believe the answer is:
droop
'languish' is the definition.
(I've seen this in another clue)
'feeble daughter about' is the wordplay.
'feeble' becomes 'poor' (feeble can mean poor or unimpressive).
'daughter' becomes 'd' (genealogical abbreviation).
'about' is a reversal indicator.
'poor'+'d'='poord'
'poord' backwards is 'DROOP'.
'to' acts as a link.
(Other definitions for droop that I've seen before include "Decline" , "Sag, hang down" , "Become limp" , "lose heart" , "Flag" .)