Like hereditary rule — and city's, oddly (8)
I believe the answer is:
dynastic
'like hereditary rule' is the definition.
(like a dynasty)
'and city's oddly' is the wordplay.
'oddly' indicates anagramming the letters.
'and'+'citys'='andcitys'
'andcitys' with letters rearranged gives 'DYNASTIC'.
(Other definitions for dynastic that I've seen before include "Relating to (ruling) family" , "Relating to line of rulers" , "Relating to a powerful family" , "Of ruling families" , "having a succession in the family" .)