Pence perhaps beginning to madden former President (4)

I believe the answer is:

mike

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'pence perhaps' is the definition.
I can't judge whether this definition defines the answer.

'beginning to madden former president' is the wordplay.
'beginning to' says to take the initial letters.
'former president' becomes 'ike' (I've seen this before).
The initial letter of 'madden' is 'm'.
'm'+'ike'='MIKE'

Can you help me to learn more?

(Other definitions for mike that I've seen before include "Singers hold this" , "Man" , "Device collecting sound from a singer, say - boy's name (abbr)" , "Boy's name - November's predecessor" , "M; man's name" .)

I've seen this clue in The Independent.

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