There are two possible options:
1 – Partial payment of the claim to the employee of what is in the account and reimburse the remaining amount when more funds become available.
2 – Hold onto the claims until the full amount is in the HSA, then reimburse in full.
If you have a large unexpected expense in the middle of a plan year, you can reimburse yourself for a portion of it with money currently in your HSA, then the following year, increase your deposits enough to cover the entire unclaimed balance. Once you have first established a Health Spending Account, you need never lose out on claiming medical expenses again.