This person's left, worker of great significance (9)
I believe the answer is:
important
'of great significance' is the definition.
(I've seen this before)
'this person's left worker' is the wordplay.
'this person's' becomes 'im' (this person means the crossword setter themselves).
'left' becomes 'port' (left side of a ship - opposite of starboard).
'worker' becomes 'ant' (worker is a type of ant).
'im'+'port'+'ant'='IMPORTANT'
(Other definitions for important that I've seen before include "Noteworthy, significant" , "Of great significance" , "major" , "essence" , "A priority" .)