Diner's companion's first to celebrate, bursting into song (9)
I believe the answer is:
cafeteria
'diner's' is the definition.
(thesaurus)
'first to celebrate bursting into song' is the wordplay.
'first to' indicates taking the first letters.
'bursting' becomes 'fete' (I am not sure about this - if you are sure you should believe this answer much more).
'into' indicates putting letters inside.
'song' becomes 'aria' (aria is a kind of song).
The first letter of 'celebrate' is 'c'.
'fete' placed within 'aria' is 'afeteria'.
'c'+'afeteria'='CAFETERIA'
'companion's' is the link.
I am not very happy about this link. It may belong to another bit of the clue.
Can you help me to learn more?
(Other definitions for cafeteria that I've seen before include "where food is served" , "Where one scoffs" , "Self-help facility" , "Self-service eatery" , "where food can be picked up" .)