Mad home — son starts to annoy nearly everyone (6)
I believe the answer is:
insane
'mad' is the definition.
('insane' can be a synonym of 'mad')
'home son starts to annoy nearly everyone' is the wordplay.
'home' becomes 'in' ('he's home' can mean 'he's in').
'son' becomes 's'.
'starts to' says to take the initial letters.
The initial letters of 'annoy nearly everyone' is 'ane'.
'in'+'s'+'ane'='INSANE'
(Other definitions for insane that I've seen before include "Out of one's mind" , "Mad, irrational" , "Mental" , "reckless" , "mad for love?" .)