The primary cells involved in the synthesis of new bone matrix are osteoblasts. These cells are responsible for the production and secretion of the organic components of the bone matrix, mainly collagen type I and other proteins that form the osteoid. Once the osteoid is laid down, it subsequently undergoes mineralization to become mature bone.

In contrast, osteoclasts play a different role; they are responsible for the resorption or breakdown of bone tissue, which is important for bone remodeling and calcium homeostasis. Osteocytes are mature bone cells derived from osteoblasts that become embedded within the bone matrix; they function primarily in maintaining the bone tissue. Chondroblasts are cells that produce cartilage matrix, not bone matrix.

Therefore, the synthesis of new bone matrix is predominantly carried out by osteoblasts.

Reference: Gray's Anatomy, 41st Edition, Volume 1, Chapter 6 / Page 215