Having a Khaleefah is a requirement for offensive Jihaad (Jihaad-e-Talab, or "Iqdaami Jihaad"). This is the Jihaad for the purpose of expanding the dominion of Islaam. Conquering of lands for Islaam. Such a Jihaad requires there to be a Khaleefah, and a Khilaafah, etc.
However, defensive Jihaad (Difaa`i Jihaad) does not require a Khaleefah. For example, the Zionist Jews attack Palestine and start killing the innocent Muslims there; men, women and children. Killing them, bombing them, arresting them, torturing them, raping the girls, starving them, so much so that there isn't even food for the people to eat. In this case, the Palestinians do not require any "Khaleefah" in order for them to fight back. They are being attacked. Standing up and fighting the Jews is Fardh (obligatory). The Zionists are the Zhaalim invaders. Such a Jihaad is known as a "Difaa`i Jihaad" (Defensive Jihaad).
If someone attacks your family, then, the `Ulamaa have written that it becomes obligatory to defend them. Some gangsters break into your house and try to rape and kill your wife and daughters. Will a person say, "No, we can't do anything. A Khaleefah is necessary for Jihaad. We must just sit still and do nothing. Let them get raped and killed." Will any sane person say this? Obviously not. Hopefully not, at least. He will most definitely get up to defend his family. This defending of his family is obligatory upon him.
Similarly, wherever Muslims are attacked and oppressed, for them to defend themselves becomes Fardh (obligatory).
Let's say Donald Trump becomes president and decides to bomb Makkah and Madeenah, for example. Will any doubt remain in the mind of any person that Jihaad becomes Fardh-e-`Ayn and every Muslim has to stand up to defend Makkah and Madeenah?
والسلام