Defence always leaky, it's Brighton's infirmity, first of all (5)
I believe the answer is:
alibi
'defence' is the definition.
(defence given to police by a suspect)
'always leaky it's brighton's infirmity first of all' is the wordplay.
'first of all' indicates taking the first letters.
The initial letters of 'always leaky its brighton infirmity' is 'ALIBI'.
(Other definitions for alibi that I've seen before include "Defence against accusation - was somewhere else" , "Lawyer's weapon, Latin for 'elsewhere'" , "Evidence of (or excuse for) being somewhere else at the time" , "Legal proof of innocence" , "Defence against accusation - was seen elsewhere at the time" .)