Impudence: slip audibly giving you mouth (3-4)
I believe the answer is:
lip-sync
'mouth' is the definition.
(I know that lip-sync is a more specific form of mouth)
'impudence slip audibly giving' is the wordplay.
'impudence' becomes 'lip' (lip is a kind of impudence).
'slip' becomes 'sin' (both can mean a mistake or failing).
'audibly' indicates a 'sounds like' (homophone) clue.
'giving' becomes 'c' (I can't explain this - if you can you should give a lot more credence to this answer).
'sin' sounds like 'syn'.
'lip'+'syn'+'c'='LIP-SYNC'
'you' acts as a link.
Can you help me to learn more?
(Other definitions for lip-sync that I've seen before include "Audio and video alignment of speech" , "Align mouth movements with recorded speech" , "Linking of speaker's mouth movements and voice in filmed recordings" .)