In one's true home that's cosy (4)
I believe the answer is:
nest
'cosy' is the definition.
(I've seen this before)
'in one's true home' is the wordplay.
'in' indicates a hidden word.
'NEST' can be found hidden inside 'ones true home'.
'that's' is the link.
(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" .)