In order to unlock a tier 3 activated skill, your Spear MUST be level 5.
In order to level it up you need to keep killing Cultists and taking the fragments they own to the ancient forge once you have enough tp upgrade.
5/5 - Level 2
5/5 - Level 3
9/9 - Level 4
9/9 - Level 5
22/22 - Level 6