About eleven come round in a state (6)
I believe the answer is:
mexico
'a state' is the definition.
(I know that Mexico is a North American country)
'about eleven come round' is the wordplay.
'about' means one lot of letters goes inside another.
'eleven' becomes 'xi' (Roman numerals).
'round' indicates an anagram.
'come' with letters rearranged gives 'meco'.
'xi' placed into 'meco' is 'MEXICO'.
'in' is the link.
(Other definitions for mexico that I've seen before include "Spanish-speaking neighbour of the USA" , "Country with both Pacific and Caribbean coasts" , "Country bordering US" , "It borders US to south" , "USA's southern neighbour" .)