I read this expression from John Adams by David McCullough,
I quitted my own carriage, and took my seat by his side[she wrote]. We rode on to Bristol, where I had previously engaged a dinner, and there upon the banks of the Delaware, we spent the day, getting into the city at sunset.
This snippet is from Abigail's dairy, documenting her meet with her husband outside Philadelphia. According to Merriam-Webster, "engage" when used as a transitive verb mostly means "attract, hold or hire". It seems I cannot find any fitting definition in this context.