No Substitute for the Divine Office
Does the Little Office of the Blessed Virgin Mary replace the mandatory Divine Office for a priest?
The obligation to recite the Divine Office is a Church precept, and therefore the particulars of the obligation are decided by the Church. The Church can permit substitutions if it so chooses.
At this time, priests obligated to recite the Divine Office cannot substitute something for the obligation. The obligation to pray the Divine Office is an obligation to pray that specific liturgy. The Divine Office is a public liturgy of the Church, not a private devotion, and, as such, changing or substituting it is akin to changing or substituting the Mass.
While the Little Office of the Blessed Virgin Mary is an ancient and venerable liturgy, it does not substitute for the obligation to pray the public liturgy of the Divine Office. The only exception to this would be if a particular religious order permits it within its own rules of life approved by the Church (Ecclesiae Sanctae 20).