Ad-lib from former European politician in shot (9)
I believe the answer is:
extempore
'ad-lib' is the definition.
(synonyms)
'former european politician in shot' is the wordplay.
'former' becomes 'ex' (prefix meaning former or onetime).
'european' becomes 'E' (abbreviation e.g. EU).
'politician' becomes 'MP' (Member of Parliament).
'in' is an insertion indicator.
'shot' becomes 'tore' ('tear' can be a synonym of 'shoot').
'e'+'mp'='emp'
'emp' going inside 'tore' is 'tempore'.
'ex'+'tempore'='EXTEMPORE'
'from' acts as a link.
(Other definitions for extempore that I've seen before include "Off-the-cuff" , "suddenly" , "without warning" , "on the spot" , "Spoken or done without preparation, impromptu" .)