How can one get away with saying a noun before a description?
警察是一个人。。。一个追逐犯人的人。 is also ok, but as you know, they are not very Chinese style.

The bad news is you can not put an attribute clause after your noun.

The good news is there are many other ways.

警察是一种专门抓犯人的人.

警察的工作是专门抓罪犯

You can use 是 to start your description, the description can be started over and over, the subject part would stay there.