One escaping English stuffiness cuts free, going topless (7)
I believe the answer is:
refugee
'one escaping' is the definition.
'english stuffiness cuts free going topless' is the wordplay.
'english' becomes 'e' (abbreviation).
'stuffiness' becomes 'fug'.
'cuts' indicates putting letters inside (some letters cut their way into other letters).
'going topless' means to remove the first letter.
'e'+'fug'='efug'
'free' with its first letter removed is 'ree'.
'efug' inserted within 'ree' is 'REFUGEE'.
(Other definitions for refugee that I've seen before include "One seeks shelter" , "Person displaced by war or disaster" , "War-forced migrant" , "One who may have left" , "One fleeing from persecution" .)