Death of director: how long to appoint a new director?

For a private ltd. company with only 2 directors, and one director is deceased on date X. Next AGM not typically due till Aug

How long does the company have before it must appoint a new director and what should be date of appointment of new director?   Same day as death of director or within 30 days? The regulations seem to be silent on number of days.

In case of death of 1 of the 2 directors, does the regulation provide a grace period?  Otherwise a pvt. ltd. needs 2 directors at anytime so what happens legally between the time of death and appointment of new director. Is co in default?

Assume director passed away on April 30th.