Important, flat device with push-button controls (6)
I believe the answer is:
keypad
'device with push-button controls' is the definition.
(device with keys on it)
'important flat' is the wordplay.
'important' becomes 'key' (similar in meaning).
'flat' becomes 'pad' (a person's home).
'key'+'pad'='KEYPAD'
(Other definitions for keypad that I've seen before include "Small unit with push buttons" , "Phone's button array" , "What might help you calculate" , "Perhaps remote" , "Typing area on an electronic device" .)