Very hot, old London district (4)
I believe the answer is:
soho
'london district' is the definition.
(area of London)
'very hot old' is the wordplay.
'very' becomes 'so' (both can mean 'extremely').
'hot' becomes 'h' (abbreviation, eg on taps).
'old' becomes 'o' (abbreviation as in OT - Old Testament).
'so'+'h'+'o'='SOHO'
(Other definitions for soho that I've seen before include "Colourful London show-biz district" , "Colourful show-biz area of West End London" , "London's former Bohemia" , "capital district" , "(Formerly) disreputable area of London" .)