They put the squeeze on Hypnos, cast outside Troy (7)
I believe the answer is:
pythons
'they put the squeeze on' is the definition.
(pythons squeeze their prey)
'hypnos cast outside troy' is the wordplay.
'cast' indicates anagramming the letters (letters are dispersed or cast around).
'outside' indicates putting letters inside.
'troy' becomes 't'.
'hypnos' is an anagram of 'pyhons'.
'pyhons' going around 't' is 'PYTHONS'.
(Other definitions for pythons that I've seen before include "Large boas" , "Idle lot" , "[SNAKES]" .)