Girl from outskirts of Liverpool grabbed by US agency (5)
I believe the answer is:
cilla
'girl' is the definition.
(woman's name)
'outskirts of liverpool grabbed by us agency' is the wordplay.
'outskirts of liverpool' becomes 'LL' (first and last letters of 'Liverpool').
'grabbed by' means one lot of letters goes inside another (inserted letters are grabbed inside).
'us agency' becomes 'cia' (I've seen this before).
'll' inserted inside 'cia' is 'CILLA'.
'from' is the link.
(Other definitions for cilla that I've seen before include "Colourful old singer" , "- Black, TV personality and singer" .)