Notice alpha male: that's first man (4)
I believe the answer is:
adam
'first man' is the definition.
(first man in the Bible)
'notice alpha male' is the wordplay.
'notice' becomes 'ad' (both can mean an advertisement).
'alpha' becomes 'a' (phonetic alphabet: alpha, bravo, charlie etc.).
'male' becomes 'm' (common abbreviation).
'ad'+'a'+'m'='ADAM'
'that's' acts as a link.
(Other definitions for adam that I've seen before include "Robert -, Sc. architect" , "expelled gardener" , "Scots. architect brothers" , "A mad sort of ancestor" , "Man No. 1" .)