Place in bedsit established (4)
I believe the answer is:
site
'place' is the definition.
(site is a kind of place)
'in bedsit established' is the wordplay.
'in' says the answer is hidden in the clue.
'SITE' is hidden in the letters of 'bedsit established'.
(Other definitions for site that I've seen before include "Locate - place" , "Situation (of a building)" , "Place for building" , "Where something is located" , "Designated place" .)