In one's true home that's cosy (4)
I believe the answer is:
nest
'that's cosy' is the definition.
(I've seen this before)
'in one's true home' is the wordplay.
'in' says the answer is hidden in the clue.
'NEST' is hidden in the letters of 'ones true home'.
(Other definitions for nest that I've seen before include "In which to lay eggs or give birth" , "Home of twigs, perhaps" , "Avian structure" , "Sent to avian home" , "Bird's house" .)