Month 1: Learn the systems. The ops hire shadows you through every process they'll own. They read the SOPs. They ask questions. They identify gaps between what's documented and what actually happens. By end of month 1, they should execute each process independently with your review.
Month 2: Own the execution. The ops hire runs the processes. You review outputs against quality checkpoints. You meet weekly (30 minutes) to discuss what's working and what needs adjustment. By end of month 2, you should be reviewing outputs, not doing them.
Month 3: Own the improvement. The ops hire identifies one process improvement per week: a step to eliminate, a template to update, a handoff that creates delays. They propose the fix and implement it after your approval. By end of month 3, the systems are better than when they started.
If the hire isn't at independent execution by day 60, one of two things happened: the SOPs weren't detailed enough, or the person isn't the right fit. Diagnose which before making a change.