Alpha male gets little bit (4)
I believe the answer is:
atom
'little bit' is the definition.
(tiny particle)
'alpha male' is the wordplay.
'alpha' becomes 'a' (phonetic alphabet: alpha, bravo, charlie etc.).
'male' becomes 'tom' (tom can mean a male cat).
'a'+'tom'='ATOM'
'gets' acts as a link.
(Other definitions for atom that I've seen before include "A tiny particle of matter with a big bang" , "Something very small perhaps" , "tiny thing" , "Small amount of matter" , "A really tiny piece of something" .)