Case containing most of bird's drink (6)
I believe the answer is:
pernod
'drink' is the definition.
(Pernod is an example)
'case containing most of bird's' is the wordplay.
'case' becomes 'pod' (pod is a kind of case**).
'containing' means one lot of letters goes inside another.
'most of' means to remove the last letter.
'bird's' becomes 'erns' (ern is a kind of bird).
'erns' with its final letter taken off is 'ern'.
'pod' enclosing 'ern' is 'PERNOD'.
(Other definitions for pernod that I've seen before include "Aniseed-flavoured liquor" , "A liqueur flavoured with anise" , "French aperitif" , "Ponder on this liqueur" , "Ponder on anis drink" .)