Short entertainment touring old part of London (4)
I believe the answer is:
soho
'part of london' is the definition.
(district of Westminster)
'short entertainment touring old' is the wordplay.
'short' means to remove the last letter.
'entertainment' becomes 'show' (show is a kind of entertainment).
'touring' indicates putting letters inside (tour can mean to go around).
'old' becomes 'o' (common abbreviation eg in OE for Old English).
'show' with its final letter taken off is 'sho'.
'sho' enclosing 'o' is 'SOHO'.
(Other definitions for soho that I've seen before include "Exotic London district popular with tourists" , "London night life area" , "Colourful London show-biz district" , "Smoke's part" , "Central London night life district" .)