Offbeat position in city's banks (6)
I believe the answer is:
cranky
'offbeat' is the definition.
(both can mean quirky or strange)
'position in city's banks' is the wordplay.
'position' becomes 'rank' (rank is a kind of position).
'in' means one lot of letters goes inside another.
'banks' means to remove the middle letters (the sides or banks of the word).
'city' with its centre removed is 'cy'.
'rank' going within 'cy' is 'CRANKY'.
(Other definitions for cranky that I've seen before include "Eccentric, odd (colloq.)" , "Crotchety" , "Eccentric - irritable" , "Ill-tempered" , "Eccentric, strange" .)