Be up against an objection (4)
I believe the answer is:
abut
'be up against' is the definition.
(to neighbour something or go beside it)
'an objection' is the wordplay.
'an' becomes 'a'.
'objection' becomes 'but' (as in 'no ifs, no buts').
'a'+'but'='ABUT'
(Other definitions for abut that I've seen before include "Cease (from activity)" , "Touch, lean on" , "Lie next to" , "Adjoin at one end" , "Adjoin, border" .)