Use its first effect to help Hazy Flame monsters in your hand to swarm the field. Then use its second effect to add Hazy Flame Peryton to your hand.
If you have any "Hazy" cards in your Graveyard upon setting this, activate it ASAP on your opponent's next turn; if they try to destroy it by a card effect, you can simply use this card's effect to add a "Hazy" card to your hand instead, wasting your opponent's destruction card.
Once you've sent this card to the graveyard via its effect, you can use Hazy Pillar's 2nd effect to make immediate use of the monster added to the hand. In a sense, this combo allows Hazy Pillar to briefly dip into your graveyard for its 2nd effect, rather than just the hand or the field.
Use this card in place of Hazy Pillar until you activate Hazy Pillar. Then get rid of it using its 2nd effect to free up your spell/trap zones.