Catch up on rest, missing island feast (7)
I believe the answer is:
banquet
'feast' is the definition.
(I know that feast can be written as banquet)
'catch up on rest missing island' is the wordplay.
'catch up on' becomes 'ban' (I can't explain this - if you can you should believe this answer much more).
'rest' becomes 'quiet' (both can mean calm).
'missing' indicates named letters should be taken away.
'island' becomes 'i'.
'quiet' with 'i' taken out is 'quet'.
'ban'+'quet'='BANQUET'
(Other definitions for banquet that I've seen before include "Ceremonial dinner for many" , "Lavish meal" , "Lavish feast" , "Grand dinner" , "Grand meal" .)