The object of having a night out? (5)
I believe the answer is:
thing
'the object of' is the definition.
The definition suggests a singular noun which matches the answer.
'a night out?' is the wordplay.
'out?' indicates anagramming the letters (out can mean wrong or inaccurate).
'night' with letters rearranged gives 'THING'.
'having' is the link.
(Other definitions for thing that I've seen before include "Object, artefact" , "Article" , "An unnamed object or item" , "Unspecified object" , "Affair - matter" .)