One breaking record for insolence? (3)
I believe the answer is:
lip
'insolence?' is the definition.
(I've seen this in another clue)
'one breaking record' is the wordplay.
'one' becomes 'i' (Roman numeral).
'breaking' indicates putting letters inside.
'record' becomes 'LP' (abbreviation for long play record).
'i' going within 'lp' is 'LIP'.
'for' acts as a link.
(Other definitions for lip that I've seen before include "Edge, rim" , "It can be read" , "Part of mouth or cheek" , "Aural impudence" , "sauciness" .)