(idiomatic) To pay a high price, especially an exorbitant or excessive amount, either in money or in some other manner.

Example: 1918, Peter B. Kyne, The Valley of the Giants, ch. 36:
  "You'll pay through the nose for this, you scoundrel," Sexton whimpered. "I'll fix you, you traitor."
1921, John Galsworthy, The Forsyte Saga, part 2, ch. 4:
  That fellow would milk the settlements somehow, and make his family pay through the nose to keep him out of bankruptcy.