Girl crossing quiet City area for a particular purpose (9)
I believe the answer is:
specially
'for a particular purpose' is the definition.
(I've seen this before)
'girl crossing quiet city area' is the wordplay.
'girl' becomes 'sally' (girl's name).
'crossing' means one lot of letters goes inside another.
'quiet' becomes 'p' (music symbol for 'piano', ie soft or quiet).
'city area' becomes 'ECI' (resembles ECs, postcode for the City of London).
'p'+'eci'='peci'
'sally' going around 'peci' is 'SPECIALLY'.
(Other definitions for specially that I've seen before include "Particularly" , "For a particular purpose" .)