Significant the man's Conservative, almost in charge (8)
I believe the answer is:
historic
'significant' is the definition.
(I've seen this before)
'the man's conservative almost in charge' is the wordplay.
'the man's' becomes 'his' (I've seen this before).
'conservative' becomes 'tory' (I've seen this before).
'almost' means to remove the last letter (most of the word but not all of it).
'in charge' becomes 'ic'.
'tory' with its final letter taken away is 'tor'.
'his'+'tor'+'ic'='HISTORIC'
(Other definitions for historic that I've seen before include "Important and/or old" , "Momentous, noteworthy" , "Redolent of past glories" , "remarkable" , "Memorable" .)