Croon about having married one foreign character (7)
I believe the answer is:
omicron
'foreign character' is the definition.
(Greek letter)
'croon about having married one' is the wordplay.
'about' indicates an anagram.
'having' indicates putting letters inside.
'married' becomes 'm' (abbreviation, e.g. in genealogy).
'one' becomes 'i' (Roman numeral).
'croon' is an anagram of 'ocron'.
'm'+'i'='mi'
'ocron' going around 'mi' is 'OMICRON'.
(Other definitions for omicron that I've seen before include "character from Athens" , "old letter" , "Greek short 'o'" , "Olympic character" , "character in Europe" .)