Strange rude minute object (5)
I believe the answer is:
demur
'object' is the definition.
(to demur is to object to something)
'strange rude minute' is the wordplay.
'strange' indicates anagramming the letters.
'minute' becomes 'm' (abbreviation).
'rude'+'m'='rudem'
'rudem' anagrammed gives 'DEMUR'.
(Other definitions for demur that I've seen before include "Waver" , "Dissent, object" , "'Object, show reluctance (5)'" , "Object gently" , "Protest mildly, show reluctance" .)