If you're still in the same browser where you made the wishlist, sign in there and it moves to your new account. If you set up a recovery link or recovery email earlier, use that. If neither applies, the wishlist can't be brought back.
A wishlist made without signing up belongs to a temporary guest account tied to your browser. Whether you get it back depends on whether that browser session still exists.
Steps
Work down this list in order.
Same browser, same device? If the guest session is still there, just sign in with Google, Facebook, or an emailed magic link. The wishlist joins your new account and you become the owner.
Saved a recovery link or email earlier? While you were still signed out you could create one. Open it to claim the wishlist. Recovery links and emails stay valid for 365 days.
Neither? Then there's no way to get it back. The next section explains why.
Why this happens
The transfer only works in the browser that still holds your guest session. Clear your cookies, switch devices, or open a private window, and that session is gone. So is the automatic transfer.
That's why a recovery link or email is the only fallback. You can only create one while you're still the signed-out owner, so set it up before you switch devices or clear anything. One catch: a recovery email won't send to an address that already belongs to a registered Wishpicks account.
Reserved a gift as a guest rather than built a wishlist? Same rule applies. See "If I reserved a gift as a guest, will it move to my account when I sign up?"
The safest move is to sign up early. Once the wishlist sits on a real account it's tied to you rather than to one browser, and you can reach it from any device.