I'm after one as an objective (3)
I believe the answer is:
aim
'an objective' is the definition.
(synonyms)
'i'm after one' is the wordplay.
'i'm' becomes 'im' ().
'after' says to put letters next to each other.
'one' becomes 'a' (a thing is one thing).
'im' put after 'a' is 'AIM'.
'as' is the link.
(Other definitions for aim that I've seen before include "Draw a bead on" , "End" , "Direct; intention" , "Set sights on, say target" , "Focus on target" .)