Tiny tips company upon a fat cat (6)
I believe the answer is:
tycoon
'a fat cat' is the definition.
(both can mean a rich and powerful person)
'tiny tips company upon' is the wordplay.
'tips' means to remove the middle letters (just the outer letters of the world).
'company' becomes 'co' (abbreviation).
'upon' becomes 'on' (I've seen this in another clue).
'tiny' with its middle taken out is 'ty'.
'ty'+'co'+'on'='TYCOON'
(Other definitions for tycoon that I've seen before include "A business magnate or wealthy industrialist" , "Rich powerful person" , "Business magnate or mogul" , "Powerful industrialist" , "Captain of industry" .)