Alpha males engaged in welcome correspondence (9)
I believe the answer is:
agreement
'correspondence' is the definition.
(synonyms)
'alpha males engaged in welcome' is the wordplay.
'alpha' becomes 'a' (phonetic alphabet: alpha, bravo, charlie etc.).
'males' becomes 'men' (man is a kind of male).
'engaged in' is an insertion indicator.
'welcome' becomes 'greet' (I've seen this before).
'men' placed inside 'greet' is 'greement'.
'a'+'greement'='AGREEMENT'
(Other definitions for agreement that I've seen before include "match" , "concert" , "deal" , "Union < matching" , "Concord, harmony" .)