How to get the Mace of Aevar Stone-Singer - Elder Scrolls: Morrowind
The Mace of Aevar Stone-Singer is given to you as a reward for completing The Skaal Test of Loyalty Main Quest on the continent of Solstheim. In order to begin this quest you'll first need to complete the 4 quests at Fort Frostmoth first; for more information check out the Bloodmoon Story Quests page at the UESP. Completing the 4 quests at Fort Frostmoth will get you the Skull of a Skaal Warrior which you'll need to show to Tharsten Heart-Fang in the Skaal Village to begin this quest.
What you need to do for The Skaal Test of Loyalty is run around the island of Solsteim and visit the 6 Ritual sites. At each site you'll need to do a mini side quest to complete the ritual. It's a long quest with many parts, use any of the guides I link to on this page for more guidance for that quest.