One slip can be local
A single slate may have lost its nail or cracked at the fixing. If the surrounding roof is sound, a local repair can be enough.
Repeated slips need a wider look
Several hooks, tabs or recently re-fixed slates across the same slope suggest that original fixings may be deteriorating more generally.
Match thickness as well as colour
A thick replacement lifts the course above it. A short slate loses overlap. A reclaimed piece can be useful, but it still has to fit properly.