Big cheese evidently satisfied mouser? (3,3)
I believe the answer is:
'big cheese' is the definition.
(I've seen this in another clue)
'evidently satisfied mouser?' is the wordplay.
'evidently satisfied' becomes 'fat' (I can't justify this - if you can you should believe this answer much more).
'mouser?' becomes 'cat' (mouser is a kind of cat).
Can you help me to learn more?
(Other definitions for fat cat that I've seen before include "(Obscenely) wealthy businessman" , "Magnate" , "Wealthy and powerful person (informal)" , "Rich man" , "Very wealthy person, especially an industrialist" .)