Well known in association with a tailless mouse (6)
I believe the answer is:
famous
'well known' is the definition.
(I've seen this before)
'in association with a tailless mouse' is the wordplay.
'in association' becomes 'fa' (I can't explain this - if you can you should believe this answer much more).
'with' says to put letters next to each other.
'a tailless' means to remove the last letter.
'mouse' with its final letter removed 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" , "Eminent" , "Illustrious" , "Renowned, noted" , "Well-known" .)