App. of cs

there is no prescribed time period you should appoint as soon as possible

According to rule 2 of  companies (appointment of Company secretary Rules) 1988, where the paid up share capital of such company is increased to required amount , the company shall, within period of one year from the date of such increase, comply with the provisions of sub- rules (1) and 2(2) of rules2.

So company secretary is required to be appointed within period of one year from the date of such increase.

Companies (Appointment and qualifications of secretary) Rules, 1988