Alpha male in charge for minute (6)
I believe the answer is:
atomic
'minute' is the definition.
('atomic' can be a synonym of 'minute')
'alpha male in charge' is the wordplay.
'alpha' becomes 'a' (phonetic alphabet: alpha, bravo, charlie etc.).
'male' becomes 'tom' (I've seen this in other clues**).
'in charge' becomes 'ic'.
'a'+'tom'+'ic'='ATOMIC'
'for' is the link.
(Other definitions for atomic that I've seen before include "of bombs" , "nuclear issues?" , "I'm Cato (anag.)" , "Realting to nuclear energy" , "Sort of bomb, number, or power" .)