After a brief party I have an excuse (5)
I believe the answer is:
alibi
'an excuse' is the definition.
(excuse given by a suspect in an investigation)
'after a brief party i' is the wordplay.
'after' means one lot of letters go next to another.
'brief party' becomes 'lib' (abbreviation for Liberal, uk political party; 'brief' asks for a short form).
'a' next to 'lib' is 'alib'.
'alib'+'i'='ALIBI'
'have' acts as a link.
(Other definitions for alibi that I've seen before include "Fact of being elsewhere (legal)" , "Legal proof of innocence" , "Suspect's excuse" , "Pretext; court excuse" , "Court evidence showing one was elsewhere" .)