Cosy home in north-eastern street (4)
I believe the answer is:
nest
'cosy home' is the definition.
'north-eastern street' is the wordplay.
'north eastern' becomes 'NE' (abbreviation).
'street' becomes 'st' (abbreviation).
'ne'+'st'='NEST'
'in' acts as a link.
(Other definitions for nest that I've seen before include "Rook's residence?" , "Snug retreat" , "Robin's home" , "Bird's retreat" , "Home for a flier" .)