praise be to Allah, the Lord of the Worlds.
In principle, tutoring is permissible, as it is an Ijarah against a lawful work. This is provided that the following rules are observed:
1-The regulations of the school where the teacher works bans private lessons. In this case, these regulations must be adhered to.
2-The tutoring doesn`t involve any violations of Sharia, such as the prohibited privacy or sedition between the two sexes.
3-The tutoring doesn`t affect the teacher`s efficiency at school. For example, he becomes negligent to force students to take private lessons, or he consumes all his mental and physical abilities in tutoring.
4-The teacher doesn`t favor tutored students over others.
In conclusion, once these rules are observed, then tutoring is permissible. And Allah the Almighty knows best.