Briefly petition British cities to move referendum (10)
I believe the answer is:
plebiscite
'referendum' is the definition.
(I've seen this before)
'briefly petition british cities to move' is the wordplay.
'briefly' means to remove the last letter.
'petition' becomes 'plea' (petition can mean to plea or beg).
'british' becomes 'b' (abbreviation e.g. in 'BBC').
'to move' is an anagram indicator.
'plea' with its last letter removed is 'ple'.
'cities' anagrammed gives 'iscite'.
'ple'+'b'+'iscite'='PLEBISCITE'
(Other definitions for plebiscite that I've seen before include "General vote" , "Public vote" , "Referendum" , "Popular vote" .)