Heads of big old organisations mainly flourish (4)
I believe the answer is:
boom
'flourish' is the definition.
('boom' can be a synonym of 'flourish')
'heads of big old organisations mainly' is the wordplay.
'heads of' suggests taking the first letters.
The first letters of 'big old organisations mainly' is 'BOOM'.
(Other definitions for boom that I've seen before include "Prosper vigorously - waterway barrier" , "Report" , "Prosperity - hollow roaring noise" , "It may protect harbour" , "Floating barrier" .)