Hi section 262 is applicable to Public Co & Pvt. Co which is a subsidiary of Public Co.. In your case it is a pvt. co so section 262 is not applicable
However for appointing any director in a board then first it is required to appoint him as an Addtional Director under Section 260 of the Companies Act read with applicable Provisions of the AOA and having been so appointed, holds office till the date of the ensuing Annual General Meeting by virtue of Section 260 of the Companies Act, 1956 read with applicable Article of the Articles of Association of the Company and is eligible for re-appointment.
1) First to appoint the director as an Additional Director in a Board Meeting.
2) To file Form 32 for his appointment as an Additional Director within 30 days of his appointment.
3) To regularized an additional director in the ensuing Annual General Meeting by passing an ordinary resolution.
4) To file Form 32 for his change in Designation i.e from Additonal Director to Director.
Thenafter he can act a regular Director.