Move south and north touring old US city (7)
I believe the answer is:
houston
'us city' is the definition.
'move south and north touring old' is the wordplay.
'move' is an anagram indicator (I've seen 'moving' mean this).
'and' is a charade indicator (letters next to each other).
'north' becomes 'N' (abbreviation).
'touring' indicates putting letters inside (touring can mean going round).
'old' becomes 'o' (abbreviation).
'south' put after 'n' is 'nsouth'.
'nsouth' anagrammed gives 'houstn'.
'houstn' placed around 'o' is 'HOUSTON'.
(Other definitions for houston that I've seen before include "One of NASA's locations" , "Tell them we have a problem" , "Texan port" , "Whitney ---, US singer" , "American place" .)