After the times of Prophet Mohammad (PBUH) there were Khalifas (representatives elected by people on consensus) who acted as "authority" or titled as "Commander/leader of the believers"...this Khilafat continued till as late as 19th century...the last Khilafat was Ottoman empire of Turkey which was dissolved in 19th century..at present there is no central leadership for the global muslim community...Each nation has their own leaders...insha Allah soon khilafat will be re-established uniting muslims all over the world again....
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There is no head of Islam religion
Islam religion is given by Allah ,the Lord of all mankind who has no assocaites or rivals and Mohammad pbuh is last messenger of Islam
It is divine religion in which Allah is supreme and Mohammad pbuh is Leader by setting up practical example on how to Submit to Allah and gain his pleasure
Another thing there is no priest or clergy in Islam and people can directly pray to Allah without intermediates
for the rest of the answer ,brother Jafar Basha answer is agreed by me .