There are three themes
United States and Postal Codes:
Unequivicably STATE state that one refuses to get along= SC,OR,NH, AR,MO, NY which includes Arizona but not Louisiana or Montana.
Of the 3 clues that are states ARIZONA = ICE is the only one in the themer.
Chemical Symbols
PERIODIC bouts of sleepwalking = S,O,Mn, Am, B,U,Li, SM of which includes Manganese but not Tungsten or Plutonious. Of the 3 clues that are elements Manganese = CREAM is the only one in the themer.
International Airports
The study of the progression of conveyances of information (such as AIR, print, or broadcast) over time MED, IAH, IST, ORY = Medina Saudi Arabia; Prince Mohammad Bin Abdulaziz + Houston, George Bush Intercontinental + Istanbul International + Paris, Ory International but doesn't include either Barcelona, J.A. Anzoategui International nor Chicago, O'Hare International. Of the 3 clues that are International Airport only Houston, George Bush Intercontinental = FLAVOR is in the themer.
Take those answers ICE + CREAM + FLAVOR and there is one clue, 19D, that is an ICE CREAM FLAVOR. 19D = Rocky Road = ORDEAL . And that is the answer.
The other trios of clues yield BIG BAND MUSIC => SWING TIME => RECESS, and THUMB NAIL PIC => ICON => HERO but as those involve items that were not in any themers they do not count.