Build majority at last (8)
I believe the answer is:
rearmost
'last' is the definition.
(I've seen this before)
'build majority' is the wordplay.
'build' becomes 'rear' (rearing is a kind of building).
'majority' becomes 'most' (most of a group).
'rear'+'most'='REARMOST'
'at' is the link.
(Other definitions for rearmost that I've seen before include "Fully behind" , "Furthest back" , "More rats (anag)" , "farthest from the front" , "last" .)