Well-known female on a tailless rodent (6)
I believe the answer is:
famous
'well-known' is the definition.
(I've seen this before)
'female on a tailless rodent' is the wordplay.
'female' becomes 'fa' (I've seen this in other clues).
'on' is a charade indicator (letters next to each other).
'a tailless' means to remove the last letter (the tail of the word is removed).
'rodent' becomes 'mouse' (mouse is a kind of rodent).
'mouse' with its last letter removed is 'mous'.
'fa'+'mous'='FAMOUS'
(Other definitions for famous that I've seen before include "Well known" , "Well-known" , "Acclaimed" , "Illustrious" , "Renowned, noted" .)