Matters awaiting attention at home: sounding characteristic (2-4)
I believe the answer is:
in-tray
'matters awaiting attention' is the definition.
(an in-tray contains documents not yet dealt with)
'home sounding characteristic' is the wordplay.
'home' becomes 'in' ('he's home' can mean 'he's in').
'sounding' indicates a 'sounds like' (homophone) clue.
'characteristic' becomes 'trait' (I've seen this before).
'trait' sounds like 'tray'.
'in'+'tray'='IN-TRAY'
'at' is the link.
(Other definitions for in-tray that I've seen before include "Tiny RA (anag.)" , "Desk point for recently arrived post" , "Desk item" , "Office work holder" , "Desktop work holder" .)