Ring American about old city (6)
I believe the answer is:
areola
'ring' is the definition.
(I've seen this before)
'american about old city' is the wordplay.
'american' becomes 'a' (common abbreviation - e.g. in organisation names).
'about' becomes 're' ('re' means regarding or about).
'old' becomes 'o' (common abbreviation eg in OE for Old English).
'city' becomes 'LA' (Los Angeles).
'a'+'re'+'o'+'la'='AREOLA'
(Other definitions for areola that I've seen before include "Ring" , "special type of circle" , "Pigmented area around a nipple" , "Circular coloured area, especially around nipple" , "Slightly sunken spot" .)