First male worker showing stubborn determination (7)
I believe the answer is:
adamant
'showing stubborn determination' is the definition.
'first male worker' is the wordplay.
'first male' becomes 'adam'.
'worker' becomes 'ant' (worker is a type of ant).
'adam'+'ant'='ADAMANT'
(Other definitions for adamant that I've seen before include "Unswerving" , "Legendary rock" , "Refusing to change opinion" , "popstar" , "Inexorable" .)