What did King Xerxes hold out to Esther so she could approach him unsummoned?

Answer: His gold scepter

Anyone approaching the king unsummoned would die unless he extended the gold scepter; Esther touched its tip.

“As soon as the king saw Queen Esther standing in the court, she found favor in his sight. The king extended the gold scepter in his hand toward Esther, and she approached and touched the tip of the scepter.”— Esther 5:2 (BSB)