If the HSA is already established but not fully funded, can future contributions be used to pay for expenses incurred after the HSA was established?

Yes. While an individual cannot use funds from an HSA for expenses incurred prior to the establishment date of the HSA, there is no statute of limitations for when a reimbursement must occur for expenses incurred after the HSA was established. This means an individual could incur an expense today and pay the provider with non-HSA personal funds and then reimburse themselves in a future year when there are funds in the HSA.