Why isn't my free gift added to the cart automatically?

Almost always because the campaign is set to Let the customer choose rather than Auto-add to cart. Those are the two options under Customer gets, and they behave completely differently on the storefront.

• Auto-add to cart — "All selected products will be auto-added to cart." Hype adds the gifts itself as soon as the cart qualifies. The customer picks nothing.
• Let the customer choose — Hype adds nothing. The customer claims the gift from the Hype: Gift Banner block, which you must add to your product page, cart page or cart drawer. Without that block on the page there is no way to claim it, and nothing happens.

You cannot have both. If you want the customer to choose one gift out of four, that is Let the customer choose with products max set to 1, and the gift banner block is required.

Check the setting in Campaigns → your campaign → Discount, on the gift rule's Customer gets panel.

Other reasons an auto-add gift does not appear

• The cart does not qualify yet. The rule's Customer buys condition — a minimum quantity or minimum amount, over all products or over selected products and collections — has to be met by the non-gift items in the cart.
• More than one gift rule. When a campaign has several rules, only the first rule whose condition is met has its gifts added.
• The gift product is not published to the Online Store. Hype reads gift products from your storefront; a product that is not available there cannot be added, and the gift block will not render.
• It was added, but the cart drawer has not redrawn. See Why does the offer only appear after I refresh the cart drawer?.
• The customer removed it. If Allow customer to remove free gift is on, Hype does not add it back. With it off, the gift is re-added.

If the offer is "buy X, get another X free"

That is the Gifts will be the same as selected products (BXGY) option. Hype adds the variant that is already in the cart back as a separate free line, in the quantity the matched tier grants, and adjusts that quantity as the cart changes. The qualifying item has to be in the cart — there is nothing for Hype to add otherwise. This option needs a quantity-based condition or Tiered gift quantities; with an amount-based condition and no tiers, nothing is added automatically.

A discount code can never add a product

If you are trying to make a code add a free gift, Shopify does not allow it: a discount code can only reduce the price of items already in the cart. That is why a customer entering the code sees it accepted as valid but not applicable. Use an automatic campaign, or a link campaign if the offer is for a specific audience.

The gift is added but not free

The gift is a product discount, so Shopify's combination rules decide whether it can also be discounted by another campaign already applying to that line. If a second discount holds the line, the gift stays at full price. See Combining discounts.

Related

• Gift with purchase
• Gift banner