Hat on Yankee supporting aristocrat's football club (5,6)
I believe the answer is:
derby county
'football club' is the definition.
(Derby County Football Club)
'hat on yankee supporting aristocrat's' is the wordplay.
'hat' becomes 'derby' (derby is a kind of hat).
'on' means one lot of letters go next to another.
'yankee' becomes 'Y' (phonetic alphabet: alpha, bravo, charlie etc.).
'supporting' is a charade indicator (letters next to each other) (in a down clue, some letters go below others).
'aristocrat' becomes 'count' (some European aristocracies have counts).
'y' put after 'count' is 'county'.
'derby' next to 'county' is 'DERBY COUNTY'.
(Another definition for derby county that I've seen is " The Rams'".)