What’ll silence buzzer going off initially when tyre’s flat (10)

'what'll silence buzzer' is the definition.
(a flyswatter might silence a buzzing fly)

'going off initially when tyre's flat' is the wordplay.
'going off' indicates anagramming the letters.
'initially' says to take the initial letters.
The initial letter of 'when' is 'w'.
'w'+'tyres'+'flat'='wtyresflat'
'wtyresflat' with letters rearranged gives 'FLYSWATTER'.