Principals of local academies refuse generous endowment - very generous (5)
I believe the answer is:
large
'generous' is the definition.
(similar in meaning)
'principals of local academies refuse generous endowment' is the wordplay.
'principals of' indicates taking the first letters (I've seen 'principal of' mean this).
The initial letters of 'local academies refuse generous endowment' is 'LARGE'.
'very' acts as a link.
(Other definitions for large that I've seen before include "Big, outsize" , "Bumper" , "Extensive" , "Massive" , "Of great size" .)