Reason heads of LEAs offer grants is controversial (5)
I believe the answer is:
logic
'reason' is the definition.
(I've seen this before)
'heads of leas offer grants is controversial' is the wordplay.
'heads of' suggests taking the first letters.
The initial letters of 'leas offer grants is controversial' is 'LOGIC'.
(Other definitions for logic that I've seen before include "subject with 14 [ARGUMENTS]" , "System of reasoning" , "Sound sense" , "using premises" , "method of reasoning" .)