Joe Biden, as the democrat president he is of course will try to push for the narrative of peace being possible in the middle east through the way of the creation of two separate states, one of the Jewish people and one of those who have Palestinian citizenship, however the problem goes beyond the creation of two states or the division of land.
it has been very clear that neither Palestine nor Israel seem to be willing to live in a peaceful convivence with their neighbors: Palestinian militias and armed groups (which are pretty much antisemitic) have already declared a prolonged war until the State of Israel completely ceases to exist, on the other hand Israel (while posing as a democratic a peace loving entity) has been trying to slowly but steadily to take over as much land as possible from Palestine. It would seem both entities do not actually seek for peace, but the total destruction of their neighbor.
I am pretty sure Netanyahu must be crossing his fingers for Donald Trump to win the election this year, the Israeli government always seeks unconditional support from the white house and the fact Biden has shown a minimum of concern over the use of the American arsenal against the innocent is Gaza is unconceivable to him.
Further events depend on who will become the future president of America, but for now the war will continue.
Unfortunately, the war against Hamas and the suffering of the Palestinian people will continue, regardless of the next president of the United States happen to be. See, the defense of Israel is one of the few bi-partisan topics which can be counted on when we talk about American politics. Both Republican and Democrats are unconditional supporters of the existence and defense of the State of Israel, the democrat just happen to be somewhat worried about the security and integrity of the innocent in the Palestinian side.
If Joe Biden gets elected he will eventually continue to send weapons and money to the IDF, perhaps less than they initially, but the flow of support won't stop. On the other hand, if Donald Trump becomes the next president of the USA, as a typical republican he is, he will completely disregard the life and well being of the Palestinian people and will continue to send as much money and weapons as possible to the IDF.
So the presidency of the USA and whoever is on the seat won't make much difference.
It would take a third party candidate to take over the presidency for something to actually to start happening in this war, and we all know that won't happen as the duopoly of politics continue in America...