Extension number given to the girl (5)
I believe the answer is:
annex
'extension' is the definition.
('annex' can be a synonym of 'extension')
'number given to the girl' is the wordplay.
'number' becomes 'x' (X is an example**).
'given to' is a charade indicator (letters next to each other).
'the girl' becomes 'anne' (I've seen this before).
'x' after 'anne' is 'ANNEX'.
(Other definitions for annex that I've seen before include "Join - add" , "Add to the end; take possession of" , "Grab" , "Attach, invade" , "Attach after conquest" .)