What happens to Element cards spent when acquiring a new Element card?
You place the cards used in the discard pile as stated in the action phase section of the rules.


  During the Action phase, you may use your Element and
  Spell cards to try to vanquish the Monster and keep it in the
  Grimoire. Five actions are possible:
  • Activate a Spell
  • Learn a new Spell
  • Acquire an Element card
  • Destroy a Curse
  • Cure one of your Madness cards
  You may take as many actions as you wish, in any order, as many
  times as you like, as long as you have the Element cards to pay for
  them. Each action costs a number of Elements, which you must pay
  by discarding Element cards from your hand or from the support
  pool or a combination of both.
  Whenever you pay an Activation Cost, you must discard enough
  Element cards to produce at least as many Elements as required
  for the action. Excess Elements spent on an Action are lost. They
  cannot be used for another Action.
  A single Element card cannot be used for multiple Actions.