In my opinion, the single director has to ensure appointing a new director and practically it will take some time, so he can run the company singly in the duration of the process.
Ensure compliances of Section 161(4) :
"if the office of any director appointed by the company in general meeting is vacated before his term of office expires in the normal course, the resulting casual vacancy may, in default of and subject to any regulations in the articles of the company, be filled by the Board of Directors at a meeting of the Board 5[which shall be subsequently approved by members in the immediate next general meeting]" Provided that any person so appointed shall hold office only up to the date up to which the director in whose place he is appointed would have held office if it had not been vacated.
and Section 174(2):
"(2) The continuing directors may act notwithstanding any vacancy in the Board; but, if and so long as their number is reduced below the quorum fixed by the Act for a meeting of the Board, the continuing directors or director may act for the purpose of increasing the number of directors to that fixed for the quorum, or of summoning a general meeting of the company and for no other purpose."