First man, social worker, resolute (7)
I believe the answer is:
adamant
'resolute' is the definition.
(both can mean determined)
'first man social worker' is the wordplay.
'first' says to put letters next to each other.
'man' becomes 'adam' (man's name).
'social worker' becomes 'ant' (ants are social insects).
'adam' next to 'ant' is 'ADAMANT'.
(Other definitions for adamant that I've seen before include "Legendary rock" , "Determined and unyielding to requests" , "With mind made up" , "Impervious to pleas or persuasion" , "uncompromising" .)