Constructed objection about one student (5)
I believe the answer is:
built
'constructed' is the definition.
('build' can be a synonym of 'construct')
'objection about one student' is the wordplay.
'objection' becomes 'but' (as in 'no ifs, no buts').
'about' indicates putting letters inside.
'one' becomes 'i' (Roman numeral).
'student' becomes 'L' (as in L-plates for learner drivers).
'i'+'l'='il'
'but' placed around 'il' is 'BUILT'.
(Other definitions for built that I've seen before include "Made by combining materials and parts" , "Erected" , "put together" , "Constructed" , "assembled" .)