Principal holds right bird (6)
I believe the answer is:
martin
'bird' is the definition.
(martin is a kind of bird)
'principal holds right' is the wordplay.
'principal' becomes 'main' (both can mean major).
'holds' means one lot of letters goes inside another.
'right' becomes 'rt' (abbreviation as in Rt Hon- the Right Honourable).
'main' going around 'rt' is 'MARTIN'.
(Other definitions for martin that I've seen before include "Man's name; bird" , "Dickens novel featuring Mr Pecksniff" , "25 across [CRANE]" , "Male name, bird" , "Swallow-like bird" .)