You shouldn’t have to go round some current American city (5)
I believe the answer is:
tampa
'american city' is the definition.
(city in Florida)
'you shouldn't have to go round some current' is the wordplay.
'you shouldn't have' becomes 'ta' (both can mean 'thank you').
'to go round' is an insertion indicator.
'some current' becomes 'amp' (electricity).
'ta' enclosing 'amp' is 'TAMPA'.
(Other definitions for tampa that I've seen before include "US town" , "City in Florida" , "Resort in W. Florida" , "Floridian resort" , "US city" .)