Excuse one vital urge with no function (5)
I believe the answer is:
alibi
'excuse' is the definition.
(excuse given by a suspect in an investigation)
'one vital urge with no function' is the wordplay.
'one' becomes 'a' (a thing is one thing).
'vital urge' becomes 'libido' (I've seen this before).
'with no' indicates named letters should be taken away.
'function' becomes 'do' (both can mean an event).
'libido' with 'do' taken away is 'libi'.
'a'+'libi'='ALIBI'
(Other definitions for alibi that I've seen before include "excuse given" , "Timely plea?" , "Suspect's excuse" , "Justification" , ""suspect's story"" .)