: For each planeswalker you control, you may activate one of its loyalty abilities once this turn as though none of its loyalty abilities have been activated this turn.The Chain Veil lets planeswalkers do more in a turn. Paying four mana and tapping it grants an additional loyalty activation for each planeswalker you control. A developed planeswalker board can use that permission for more cards, removal, loyalty, or progress toward an ultimate, making the artifact scale with the number of walkers present.
The activation does not untap anything or provide the mana to use itself again. Untap effects and strong mana production are separate pieces when building repeated-activation sequences. Teferi, Temporal Archmage is a notable partner because its minus ability can untap permanents, including mana sources and the Veil. Whether a loop works depends on the available mana and loyalty resources.
The extra permission also does not remove ordinary timing restrictions on loyalty abilities by itself. Most planeswalkers still activate during your main phase with an empty stack unless another effect changes that. Keep the timing distinct from the number of activations allowed.
A simple fair use is activating two different planeswalkers, activating the Veil, and using another loyalty ability from each. You may choose different abilities on the second activations, but must still pay the loyalty costs. Extra permission does not grant loyalty counters to fund a minus ability.
At your end step, the Veil causes two life loss if you did not activate a loyalty ability that turn. That is usually manageable in a dedicated planeswalker deck but reinforces how specialized the artifact is. Four mana to cast and another four to activate is a large setup cost for only one modest walker. Establish several useful loyalty abilities or a specific untap engine so the additional activations justify the resources spent.
