Rush to suppress a cry of delight (6)
I believe the answer is:
hurray
'cry of delight' is the definition.
(hurray!)
'rush to suppress a' is the wordplay.
'rush' becomes 'hurry' (synonyms).
'to suppress' means one lot of letters goes inside another (inserted letters are suppressed or crushed).
'hurry' placed around 'a' is 'HURRAY'.
(Other definitions for hurray that I've seen before include "Yippee!" , "cheer" , "very brief message of joy" .)