The doctor is a popular bird! (6)
I believe the answer is:
intern
'the doctor' is the definition.
(intern is a kind of doctor)
'popular bird' is the wordplay.
'popular' becomes 'in' ('in' can mean trendy).
'bird' becomes 'tern' (tern is a kind of bird).
'in'+'tern'='INTERN'
'is a' is the link.
(Other definitions for intern that I've seen before include "(American) hospital doctor" , "Deprive of freedom" , "put in jail" , "Official language of Pakistan" , "22 [IMPRISON]" .)