Between 656 and 661 Ali (RAA) was kaliph, during one of the more turbulent periods in Muslim older time, which also agreed with the First Fitna.
Uthman’s murdered meant that insurgent had to choose a new Kaliph because his most followers were insurgent. However, when some distinguished friend s of the prophet (PBUH) in extra to the population of Medina advised him to accept the present, he lastly agreed.