At heart, realise rabies might constitute an excuse (5)
I believe the answer is:
alibi
'an excuse' is the definition.
(excuse given by a suspect in an investigation)
'at heart realise rabies might' is the wordplay.
'at heart' means to look at the middle letters.
'rabies might' becomes 'bi' (I can't explain this - if you can you should give a lot more credence to this answer).
The centre of 'realise' is 'ali'.
'ali'+'bi'='ALIBI'
'constitute' acts as a link.
This may not be right. It may belong to another bit of the clue.
Can you help me to learn more?
(Other definitions for alibi that I've seen before include "Defence that one was somewhere else at the time of a crime" , "in order to prove I was elsewhere" , "excuse given" , "Excuse - plea of being elsewhere" , "Courtroom evidence" .)