Made objection, having one left (5)
I believe the answer is:
built
'made' is the definition.
(building is a kind of making)
'objection having one left' is the wordplay.
'objection' becomes 'but' (as in 'no ifs, no buts').
'having' means one lot of letters goes inside another.
'one' becomes 'I' (Roman numeral).
'left' becomes 'l' (common abbreviation).
'i'+'l'='il'
'but' placed around 'il' is 'BUILT'.
(Other definitions for built that I've seen before include "put together" , "Erected" , "assembled" , "Constructed" , "Raised" .)