Cleric’s right to run round City area (6)
I believe the answer is:
rector
'cleric's' is the definition.
(I've seen this before)
'right to run round city area' is the wordplay.
'right' becomes 'r' (common abbreviation).
'run' becomes 'r' (cricket abbreviation).
'round' means one lot of letters goes inside another.
'city area' becomes 'EC' (EC is a London postcode area).
'r'+'to'+'r'='rtor'
'rtor' going around 'ec' is 'RECTOR'.
(Other definitions for rector that I've seen before include "Parish clergyman" , "Cleric" , "Preacher Man" , "Vicar" , "Parish priest" .)