Dear Vicky
In the case give by you, if there is already 12 numbers of directors in the Comapny and if the company needs to appoint Mr. Z as additional Director than the company certainly require the Central Government Approval before doing this.
Otherwise Mr Z can be appoint as an Additional Director just by passing a Board Resolution. No need for Resolution at General Meeting.
The concept of additional director:
In the normal case every company is intended to appoint director by the procedure laid down in the Companies Act so as utilise the full three years of services of such person as Director.
If there is any urgency to appoint Director the Act gives relaxation from the normal procedure by inserting Section 260.
Regards/ Akhil Gupta