First, check that you have the latest version of the Hailo app - Apple Pay is only available in version 4.22 or above. If you still don’t see Apple Pay as a payment option in the "Paying With" section, it either means that Apple Pay is not set up on your phone, or that you have selected an American Express card as your Apple Pay card. Please select a VISA or Mastercard credit or debit card in order to use Apple Pay.
See here and here for more information about using Apple Pay with Hailo.
Apple Pay will not show as a payment option in your Wallet until you have paid for your first Apple Pay journey.