At home quiet, we hear: drop in (6)
I believe the answer is:
instil
'drop in' is the definition.
(I've seen this before)
'at home quiet we hear' is the wordplay.
'at home' becomes 'in' ('I'm in' can mean 'I'm at home').
'quiet' becomes 'still' (synonyms).
'we hear' shows a homophone (sound like).
'still' sounds like 'stil'.
'in'+'stil'='INSTIL'
(Other definitions for instil that I've seen before include "Inculcate" , "Put in drop by drop" , "Implant (in the mind)" , "Inject ideas into mind" , "Infuse (something) slowly into the mind" .)