No, it is not necessary to appointment independent director for all types of companies.
According to section 149(4) read with Rule 4 of companies (Appointment and qualification of Directors) Rules, 2014. The below mentioned are the companies needs to appoint a independent director.
1. All listed companies. 2. Other public companies having
Paid up capital of ₹10cr or more. or Turnover of ₹100cr or more. or Outstanding loans, debentures and deposits of ₹50cr or more.
"Private limited companies no need to appoint independent director".