When was the last time you saw a skink in Otautau? This skink was seen sunning itself a few days ago in a friend's yard. It's a Common Skink but they are very uncommon these days due to predation by cats and rats as well as lack of good habitat.
You may be surprised to know that skinks eat berries and nectar and so planting these kinds of plants in your yard may help give skinks a better chance of survival. They also need places to hide from predators. They need debris, old logs and things to escape into. Wide open paddocks with very short grass or very tidy gardens have created a dire landscape for skinks. So a messy yard isn't a bad thing.
This particular skink may have had a narrow escape from a cat. You can see the line break on his body where his new tail has grown. You can't expect your cat to stop hunting but maybe there is something else you can do.
To make your yard skink-friendly, read these DoC guides. The first is written for the Wellington area but the principles apply anywhere.
Lizards in Your Garden (pdf, 1.5MB)
Skinks and Geckos Factsheet (pdf, 220kb)