I say, and with God's success: If the imam fears missing the Eid prayer and begins it while in a state of ritual purity (tayammum), it is not permissible; because someone like him should be waited for. If they pray, he has the right to repeat it. Refer to: رد المحتار 1: 161, and شرح ابن ملك ق13/أ. It was validated by the author of الهداية 1: 27, and الخانية 1: 63, and النسفي in الكافي, and God knows best.