City shelter — doss on the outside (5)
I believe the answer is:
leeds
'city' is the definition.
(Leeds is an example)
'shelter doss on the outside' is the wordplay.
'shelter' becomes 'lee' (I've seen this before).
'on the outside' suggests removing the centre.
'doss' with its middle taken out is 'ds'.
'lee'+'ds'='LEEDS'
(Other definitions for leeds that I've seen before include "Yorks city" , "City near Bradford" , "22 [FA CUP] runners-up" , "City on River Aire" , "Industrial city of northern England" .)