Which hormone increases osteoclast activity to release more calcium ions into the bloodstream?

both parathyroid hormone and calcitrol.

Explanation:

In the body calcium homeostasis, which is generally defined as the maintenance of specific internal conditions, is mediated by the endocrine system through hormonal control; hormones are usually specialized signal molecules derived from lipids or amino acids. This regulates the calcium flux between the bloodstream and the bone; and the hormones responsible, change the ratio of osteoclast activity to osteoblast activity -osteoblasts build bone while osteoclasts breakdown or degrade bone.

Hormones responsible include calcitonin (from special parafollicular cells in the thyroid gland), cacitrol (activated vitamin D) and the parathyroid hormone (from the  parathyroid glands).  These affect the absorption of calcium from the gut, or kidney reabsorption; both parathyroid hormone and calcitrol act by causing the release of calcium ions into the bloodstream as the bone is degraded by osteoclasts.