The Israel Discount Bank, known as IDB Bank, will be leaving its longtime digs at 511 Fifth Ave. on the southeast corner of East 43rd Street — and up and into the Grace Building, a block over on Sixth Avenue.

Sources say when it moves, the bank will have its own entrance through the Kreuther chocolate store at 43 W. 42nd St. The new digs will include the second floor — formerly occupied by HBO — which boasts high ceilings and huge windows overlooking Bryant Park.

Altogether, IDB’s new spread, which also includes the eighth and ninth floors and part of the 10th, will span nearly 125,000 square feet.

For many years, IDB has occupied the entire building at 511 Fifth Ave. Built in 1915, the structure is controlled by Jeff Sutton and Aurora Capital on a long-term ground lease to mid-2114.

IDB wanted something special to change its image, according to a source. The space is yet to be built out.

Lance Korman, Brian Waterman and David Berke of Newmark Knight Frank represented IDB.

A CBRE team led by Peter Turchin is the brokerage for the Grace Building, while Duncan McCuaig negotiated in-house for the Brookfield ownership.

Asking rents have been hovering at $100 per square foot.