Note about old hotel in central London area (4)
I believe the answer is:
soho
'central london area' is the definition.
(Soho is an area of Central London)
'note about old hotel' is the wordplay.
'note' becomes 'so' (musical note).
'about' is an insertion indicator.
'old' becomes 'o' (common abbreviation eg in OE for Old English).
'hotel' becomes 'h' (phonetic alphabet: alpha, bravo, charlie etc.).
'o'+'h'='oh'
'so' going around 'oh' is 'SOHO'.
'in' acts as a link.
(Other definitions for soho that I've seen before include "Hunter's announcement of sighting a hare" , "Colourful neighbourhood in London's West End" , "Once notorious part of central London" , "Colourful district in central London" , "Smoke's part" .)