State secrets in British science establishment (4)
I believe the answer is:
blab
'state secrets' is the definition.
(to blab is to reveal or state a secret)
'british science establishment' is the wordplay.
'british' becomes 'b' (abbreviation e.g. in BBC).
'science establishment' becomes 'lab' (laboratory).
'b'+'lab'='BLAB'
'in' acts as a link.
(Other definitions for blab that I've seen before include "Shoot one's mouth off" , "Give the game away" , "Reveal secrets by indiscreet talk (colloq.)" , "Give away secrets" , "Let the cat out of the bag" .)