Rachel searched around part of London (7)
I believe the answer is:
chelsea
'part of london' is the definition.
'rachel searched around' is the wordplay.
'around' indicates a hidden word.
'CHELSEA' is hidden in the letters of 'rachel searched'.
(Other definitions for chelsea that I've seen before include "Type of sugared currant bun" , "Team in blue" , "London borough with annual Flower Show" , "Sort of bun" , "Part of Manhattan" .)