Mayor de Blasio tapped Children’s Aid Society CEO Richard Buery Jr. as his fourth and final deputy mayor Tuesday — even as City Hall mulls booting the group’s charter school from a public building.

In his new role, Buery’s duties will include pushing for the mayor’s signature bid to expand full-day pre-K, an initiative that’s poised to compete with charter schools over scarce public-school space.

Yet as head of the nonprofit, Buery, 42, had lobbied for the Children’s Aid College Prep Charter School to be granted temporary space inside a South Bronx building that also houses two traditional public schools.

Still, the appointment of a charter-school ally to City Hall — and of an accomplished graduate of Harvard and Yale Law School — gave charter supporters some hope.

“I think Richard has such a commitment to public education in all forms, and . . . understands that we need partnerships between community-based organizations, district schools [and] charter schools,” said New York City Charter School Center CEO James Merriman.