One slate can be a small repair
If the rest of the roof is secure, a single slipped slate can often be re-fixed or replaced without disturbing a large area.
Several slips need more thought
If slates keep moving from different parts of the same slope, old nails or fixings may be failing more widely.
The replacement has to sit properly
The new slate needs the right length and thickness so that it lies flat with the surrounding courses and keeps the correct overlap.