Is there any agreement between Israel and the United States that could force the U.S. to become a belligerent for Israel in a war? The U.S. was never a direct participant in a war Israel fought and that was considered as a war by the Israeli Ministry of Defense, but my question is if there's a clause in one of the numerous agreement between the U.S. and Israel that would force the United States of getting involved directly just like how a clause in NATO forces all NATO countries to wage a war against a country if the country attacks one of its members.
Is there any agreement between Israel and the United States that could force the U.S. to become a belligerent for Israel in a war?
The U.S. has no such defense treaty with Israel. Israeli PM's have discussed it but internal Israeli considerations have always stopped the negotiations short of a treaty. Israel has long felt such a treaty would restrict their actions in the face of troubles. Also a consideration was Israel not wanting to involve itself in US's broader security concerns.
Israeli Prime Minister David Ben-Gurion sought to sign a defense treaty with the United States as early as the 1950s. Since then, Prime Ministers Rabin, Peres, and Barak have considered this a form of security and political compensation for Israel, in exchange for the concessions that would be involved in peace agreements with the Palestinians or Syria, and a way to mitigate the price of the concessions among Israeli public opinion. Prime Minister Netanyahu also raised the idea September 2019 Israeli election. Nonetheless, the security establishment has traditionally objected to a defense treaty.
The opposition to a defense contract with the US rests primarily on the fear that Israel will lose its freedom of action and would be bound by a reciprocal commitment to assist the United States around the world and support its global policy, for example, toward China, Russia, and Ukraine. However, in practice, the cooperation between Israel and the United States is already so deep that Israel rarely takes any military or political actions of consequence without first consulting with the United States, and in practice, seeking its approval. Already today Israel supports the United States’ global policy. As an official ally, Israel's access to advanced American weaponry and unique technologies would be guaranteed for the long term, thereby maintaining Israel’s qualitative military edge over time.
As far as I know, no, but the question is also pointless. In NATO Article 5, all members promise to consider any attack on one of them an attack on all of them, and to take
[...] such action as it deems necessary, including the use of armed force, to restore and maintain the security of the North Atlantic area.
The EU Treaty 42.7 is arguably stronger, but of course it does not include the US.
Both sets of promises rely on the political credibility of the nations making the promises. Israel has no NATO membership, so the question is how credible US support for Israel is in the absence of such a signed and ratified treaty.
A treaty can reinforce credibility, but it is not enough. Much more relevant are military structures, and exercises, and ultimately tripwire forces like those on the Iron Curtain during the Cold War and today in the Baltics (note how many countries those include, to the detriment of military effectiveness). Even so, the UK decided to get nuclear weapons which it can launch independently, and France decided to get nuclear weapons which it can launch and maintain independently.
Does the absence of a treaty commitment towards Israel mean there will be no support? The question would be if it is politically thinkable that the US and NATO would let Israel be overrun if they can prevent it through military action. To answer that, one would have to gauge the policies of the current US President, of the current majority in Congress, and of future elected leaders. Right now, the deployment of aircraft carriers to the region is a strong political sign that "all options are on the table," as the US puts it. The US also designated Israel a major non-NATO ally, and passed laws which require special considerations of Israeli security in any arms sales to other countries in the region. Another strong political sign, and one which has lasted much longer than just the current administration.
Yet Israel decided not to fully trust the future reliability of the US, and to get nuclear weapons for themselves. This came at a great political and financial price, but Israel decided to pay it.