You have both options! You can pay at the counter each time, or pay through the OneNUHS app (formerly NUHS app). The app lets you view and pay your outstanding outpatient bills, and you can even download the bills for insurance claims.
If you want to skip the queue, they also have an Auto-pay feature where you register a credit/debit card (Visa/Mastercard) and it auto-charges for selected outpatient services so you don’t have to queue to pay each visit. Quite convenient! You can set that up in the app under your profile. Bills usually show up in the app within a few days after your visit.