Even when mentioning the state motto, she avoided the Latin word, “excelsior,” which Mr. Cuomo was fond of repeating. She instead used the translation: ever upward, saying, “It’s who we are and where we’re going.”

Indeed, Mayor Bill de Blasio of New York City and many members of the State Legislature have welcomed Ms. Hochul’s rise with a sigh of relief after years of feuding with Mr. Cuomo, whose ruthless governing style and overbearing presence led many members of his party to work with him out of intimidation, rather than good will.

Ms. Hochul vowed to move with urgency on

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