Well-known fellow with a tailless rodent (6)
I believe the answer is:
famous
'well-known' is the definition.
(I know that well-known can be written as famous)
'fellow with a tailless rodent' is the wordplay.
'fellow' becomes 'fa' (I can't justify this - if you can you should give a lot more credence to this answer).
'with' 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 final letter taken off is 'mous'.
'fa'+'mous'='FAMOUS'
Can you help me to learn more?
(Other definitions for famous that I've seen before include "Known and esteemed" , "Illustrious" , "Well known" , "Widely-known" , "Eminent" .)