Today, while its possible to accept a gift card or dollar credits for a renewing membership's initial payment, there currently isn't a way to have its remaining balance applied to future renewals automatically.
There is, however, a workaround that will allow you to:
accept the initial payment using a gift card
comp a specific number of upcoming renewals based on the gift cards balance
zero out the remaining gift card balance
Note that you can apply dollar credits instead of using a gift card by navigating to a customer's profile, checking to see how many dollar credits they have just below their name, then editing the future renewals down by the same amount.
Take payment for the first membership renewal with the gift card
Click home > POS > select the customer, add the membership to the cart > select gift card > enter the code > Before you submit the sale,
note the 'amount left' on the gift card (If the amount left is $150, and the sale you're about to perform is $50, the remaining balance will be $100) > copy the gift card code before Submitting the sale, and remember the new balance (you can always retrieve this figure from Studio Setup > Gift Cards later.
Next, comp the customer's upcoming renewals based on the gift cards new remaining balance.
Navigate to the customer's profile via Customers > Customer List > select the customer > locate their membership > click the dropdown menu to the right > Edit
Update the scheduled payments by zeroing them out by the amount of the remaining balance. Ie. if there's $100 left on the card and the membership costs 50 a month, zero out the next two months.
Important: after making changes, make sure to scroll to the bottom of the pop up to save these changes.
Next, zero out the remaining gift card balance
Click Studio Setup > Gift Cards > search for the gift card number by pasting it into the search bar > zero it out
Lastly, make sure the customer has added a card on file (from their profile, click the Actions menu in the top right. You can add their card info from this menu or you can have them log in on their own time to momence.com to handle this.) Having a card on file will ensure they get to keep their membership benefits when the first charge hits.