Extremely small and quiet nursing home (6)
I believe the answer is:
minute
'extremely small' is the definition.
(I've seen this before)
'quiet nursing home' is the wordplay.
'quiet' becomes 'mute' (I've seen this in other clues).
'nursing' indicates putting letters inside.
'home' becomes 'in' ('he's home' can mean 'he's in').
'mute' going around 'in' is 'MINUTE'.
'and' is the link.
(Other definitions for minute that I've seen before include "Very small, like unit of time" , "Little -- 60 18 across" , "Precise" , "Tiny - proportion of time" , "Brief note" .)