Exchange time must be used in the fiscal year it is earned (e.g., fiscal year 2022 is July 1, 2021 through June 30, 2022; time earned during the year must be used by June 30th).
If you have time available in your Exchange bank at the beginning of June, EmpCenter shows that if you do not use the time by June 30th, you will lose the time:

If you click on the Show Details link you will see that EmpCenter is set to “Clear” the bank on June 30th:

You are still able to use that time during the month of June – up to and including on the 30th:

Any balance remaining at the end of the day on the 30th will clear from your leave bank.
If you earn Exchange time in the last 90 days of the fiscal year, you may be able to carry the time forward. See the SEIU Collective Bargaining Agreement for more details.