Hammer of Proving

The Hammer of Proving is the Season of the Chosen progression item, unlocked after the Challenger's Proving questline and Battleground: Hailstone on Europa. It is kept in your quest tab and returns to the War Table in the H.E.L.M..

Charging

You need Cabal Gold to forge a Challenger Medallion, which costs 14 Cabal Gold and is slotted into the hammer. Cabal Gold is earned from playlist activities, public events, the Blind Well or The Altars of Sorrow. Launch Battlegrounds from the Vanguard menu, and three extra chests appear beside the normal reward chest at the end. Each fireteam member opens one for gear and a hammer charge. The hammer holds up to three charges.

Umbral Engrams

At the Prismatic Recaster in the H.E.L.M., combine one charge, five legendary shards and an Umbral Engram to get a focused Umbral.

War Table upgrades

Upgrading the War Table increases the Cabal Gold you can hold and the number of charges the hammer can store. Its enhancements unlock through War Table rank, which rises with weekly challenges. The best-rated upgrades include the Tribute Chest enhancements, which give extra gold, and Proving Rune III, which gives a chance at an extra charge.

These sources describe the system as it worked in Season of the Chosen, so later seasons may differ.