Last close majority (7)
I believe the answer is:
endmost
'last' is the definition.
(similar in meaning)
'close majority' is the wordplay.
'close' becomes 'end' (close can mean to end or finish).
'majority' becomes 'most' (most of a group).
'end'+'most'='ENDMOST'
(Other definitions for endmost that I've seen before include "extreme situation" , "Last in the line" , "Furthest away" , "final" , "Last in a row" .)