During the chapter "From the Shadows" you learn that you can use your collected Artifact Fragments for upgrading your Spear of Leonidas!!
Herodotos and Barnabas will lead you to Andros island. There you will discover the Ancient Forge. Use your Spear to gain entry. Then walk to the back of the enormous area to find a spot where you can place the Spear and get it upgraded. Look for this mold shaped like a spear.
It costs artifact fragments for each upgrade. To get more fragments, you need to hunt down more Cult members. Consult the Cultists page and your map to aid your hunt. Hover over "Upgrade the Spear" on the Quests page to see how many fragments you still need for your next level. According to Seeker74
, you have to leave the cave and finish the quest that brought you there before the new quest "Upgrade the Spear" will show up in your quest list.
Level 1 (default)
Level 2 requires 1 fragment
Level 3 requires 3 fragments
Level 4 requires 7 fragments
Level 5 requires 9 fragments
Level 6 requires 22 fragments
Each upgrade could increase one or more of the following:
•Health gained per Adrenaline spent
•Max Adrenaline segments
•Max Ability rank
•Number of Ability Wheels unlocked
thanks to rene keijzers
and Dr Zoidstein
for confirming info