Posh boys regularly rejected in part of London (4)
I believe the answer is:
soho
'part of london' is the definition.
(district of Westminster)
'posh boys regularly rejected' is the wordplay.
'regularly' means one should take alternating letters (regularly take one letter, leave next etc.).
'rejected' says the letters should be written backwards.
'posh'+'boys'='poshboys'
The alternate letters of 'poshboys' are 'ohos'.
'ohos' written backwards gives 'SOHO'.
'in' acts as a link.
(Other definitions for soho that I've seen before include "W London area" , "London's nightlife centre" , "Central London or Manhattan district" , "District of London, noted for restaurants and nightclubs" , "Colourful London show-biz district" .)