Can I take an examination of Wugang's teacher establishment after the examination in Xinning?

You can't. The establishment of teachers is aimed at the establishment of the education system in each education administrative region, and each region has its own regulations on recruiting and hiring teachers. Usually, the teacher establishment in one area cannot be directly transferred to another area. Therefore, after obtaining the teacher establishment in Xinning, if you want to be a teacher in Wugang area, you need to take the local teacher recruitment examination and pass the relevant selection procedures. So I suggest you know the specific policies and requirements of the target area.