The line of imams of the Mustali Ismaili Shia Muslims (also known as the Bohras/Dawoodi Bohra) continued up to Aamir ibn Mustali. After his death, they believe their 21st Imam Taiyab abi al-Qasim went into a Dawr-e-Satr (period of concealment) that continues to this day. In the absence of an imam they are led by a Dai-al-Mutlaq (absolute missionary) who manages the affairs of the Imam-in-Concealment until re-emergence of the Imam from concealment. Dawoodi Bohra's present 53rd Da'i al-Mutlaq is His Holiness Syedna Mufaddal Saifuddin (TUS) who succeeded his predessor the 52nd Da'i al-Mutlaq His Holiness Syedna Mohammed Burhanuddin (RA). Furthermore, there has been a split in the Dawoodi Bohra sect which has led to the formation of Qutbi Bohra sect which was formed and led by Khuzaima Qutbuddin.
Who are the Bohras led by in the absence of an imam?
Dai-al-Mutlaq