Stay on the ground
Check roof slopes, ridges, verges and gutters with binoculars or phone zoom if useful. Pieces on the garden or pavement can tell you what came loose. Do not climb onto a wet roof after a storm.
Secure before perfect
A temporary weathering repair may be the right first step if the roof is still leaking and proper access or matching materials are not available. Make sure everybody knows it is temporary.
Wind exposes old weakness
The storm may be when a nail finally gives way, not when corrosion began. One moved slate therefore justifies checking the surrounding fixings while access is available.
Keep the photographs
Pictures before and after work help show what changed. They are also useful if a different leak later appears in the same area.