Cross into western half of Europe, second-rate out-of-town area (5)
I believe the answer is:
exurb
'out-of-town area' is the definition.
(I've seen this before)
'cross into western half of europe second-rate' is the wordplay.
'cross' becomes 'x' (X is cross-shaped).
'into' indicates putting letters inside.
'western half of' suggests halving the letters.
'second rate' becomes 'b'.
'europe' cut in half is 'eur'.
'x' going within 'eur' is 'exur'.
'exur'+'b'='EXURB'
(Other definitions for exurb that I've seen before include "rich residential area" , "stockbroker belt" , "out-of-town area" , "Sell this US town's rich outskirts" , "District outside city" .)