Put in the oven for 20/30 minutes until the top is nicely browned.
Remarks
For a more sophisticated recipe, you can:
Make more than 4 layers of mashed potato-meat-mashed potato-cheese, for example mashed potato-meat-mashed potato-cheese-meat-mashed potato-cheese. You should, of course, finish with a layer of mashed potato sprinkled with cheese.
Add some cream to the mashed potatoes
Add some chopped ham or bacon to the meat
It is worth noting that French "purée" is softer and much richer that traditional British "mash", so makes more of a gratin topping than a pie crust.