Institutes needing no area for meals (7)
I believe the answer is:
lunches
'meals' is the definition.
(I know this)
'institutes needing no area' is the wordplay.
'institutes' becomes 'launches' (institute can mean to start or launch something).
'needing no' indicates named letters should be taken away.
'area' becomes 'a' (maths abbreviation).
'launches' with 'a' taken away is 'LUNCHES'.
'for' is the link.
(Other definitions for lunches that I've seen before include "Midday meals" , "Dines" .)