Keen to take cut around four (8)
I believe the answer is:
incisive
'keen' is the definition.
('incisive' can be a synonym of 'keen')
'cut around four' is the wordplay.
'cut' becomes 'incise' (incising is a kind of cutting**).
'around' means one lot of letters goes inside another.
'four' becomes 'iv' ('IV' can be a synonym of 'four').
'incise' going around 'iv' is 'INCISIVE'.
'to take' is the link.
(Other definitions for incisive that I've seen before include "Of speech, sharp and clear" , "Analytical, concise" , "Intelligently analytical and clear-thinking" , "Clear and probing, trenchant" , "Piercing" .)