Pence perhaps beginning to madden former President (4)
I believe the answer is:
Here is my best explanation:
'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'.
(Other definitions for mike that I've seen before include "Sound receiver", "Man", "Device collecting sound from a singer, say - boy's name (abbr)", "Boy's name - November's predecessor", "that helps speaker to be heard", "letter in code", "Comms code for M", "Device for converting sound waves to an electronic signal (abbr)", "may need this to speak" and "Code word for M".)