How can I get more ancient arrows?

Ancient Arrows can also be obtained:

• In 9 treasure chests in Hyrule Castle - three have 1 arrow, five have 3 arrows, and one has 5 arrows.
• At Akkala Ancient Tech Lab for purchase after reactivating the blue flame furnace as per Eduardo Melzer's answer.
  • 1 arrow costs 90 Rupees, 2 Ancient Screws & 1 Ancient Shaft.
  • 3 arrows cost 250 Rupees, 6 Ancient Screws & 3 Ancient Shafts.
  • 5 arrows cost 400 Rupees, 5 Ancient Springs, 5 Ancient Shafts & 5 Arrows.

You can buy ancient arrows at the Akkala Ancient Tech Lab, after reactivating the furnace with blue flame