He supplements his income by giving private lessons.

他当家庭教师以补充收入。

《牛津词典》

Mother gives private lessons to supplement her income.

妈妈给私人授课以贴补收入。

youdao

Then the child has private lessons all the year round.

然后，小孩子就好像是一年到头地由家庭教师授课。

youdao

The school offered her private lessons instead.

VOA: special.2009.11.30

Amelio hired a Chinese coach to give him private lessons in his Singapore home.

FORBES: Not East or West

Trapezium, located in northeast Montreal, offers regular daily classes as well as private lessons in the art of trapeze.

BBC: Run away to the circus in Montreal

Granted, there were only 4 sessions a year, but Eric also offered private lessons not sanctioned by the prison.

FORBES: Mortgage Brokering Taught in Prison