There are a few ways to do this and to make it beneficial to the parent and the baby.
If the breast feeding parent pumps two to three times a day after a breastfeeding session to save for the night, the baby should have plenty of milk during the night and doing this will increase the parent’s milk supply. If the parent does not produce enough milk, supplementing with formula for a couple of night feedings is fine too.
Another way to continue to breastfeed through the night while having NCS care would be for the NCS to bring the baby to the parent for feeding throughout the night and after the feeding, the parent passes the baby back to the NCS to be burped, a diaper changed and put back to bed.
The third way would be to breastfeed during the day and formula feed during the night. The breastfeeding parent would still have to pump a time or two during the night though to keep up with and encourage milk supply to continue to increase. NCS is usually very open to any new ideas that might work better for a particular family so feel free to share your wants and wishes with them in order to make breastfeeding work for you and your baby.