Bird in apartment on right (6)
I believe the answer is:
condor
'bird' is the definition.
(condor is a kind of bird)
'apartment on right' is the wordplay.
'apartment' becomes 'condo' (I have seen 'American apartment' mean 'condo' so perhaps 'apartment' could also mean 'condo').
'on' is a charade indicator (letters next to each other) (in a down clue, letters appear on others).
'right' becomes 'r' (common abbreviation).
'condo'+'r'='CONDOR'
'in' is the link.
(Other definitions for condor that I've seen before include "Large vulture of S America" , "Large flyer" , "Largest New World vulture" , "Large American vulture" , "Andean vulture" .)