"Washington would set a precedent, ...."
Understanding this clause all depends upon understanding the words "would" and "precedent." A technical definition of would is that it is a modal, indicating grammatical mood, indicating the past tense in the subjunctive mood of the auxiliary verb will. Well. What this means is that would expresses a desire, an intent, a wish for something to come about in the future but that has not happened yet. This establishes would as a conditional: If something happens (a condition), then something else will or may happen (a result). Usually, would appears in one clause, the conditional clause, that is paired with a second clause, the result clause, but your quote shows only the conditional clause.
Here's an example of how all this comes together. Let's say that last year, I wished or intended to establish a club, then found a sponsor. I can express this in the subjunctive mood using the past tense modal auxiliary form of the verb will (which is would) by writing: "I would establish a club, ...." Apply this to Washington's statement and we see that Washington at one time wished or intended to set a precedent. Now--what is a "precedent"?
Precedent is a term often associated with legal settings. It means to set a rule or a benchmark that sets or determines how similar future events or circumstances will be handled. To explain this, Washington encountered many instances that no other had ever faced before, thus he had to determine the right course of action. His options included (1) following actions that had gone before in similar events or circumstances or (2) taking new actions, setting new paths to follow, making new decisions, in other words, breaking with tradition.
What this tells us when applied to the quote is that Washington wished or intended to take new action or make a new decision that broke with tradition for the purpose of setting a new rule for a new tradition for others to follow in the future. To put it another way, Washington would wish or intend to set a precedent thus making a new way to decide actions in future similar events or circumstances. We see that using a well understood would and precedent in a conditional clause allows for great economy of words that produces the most elegant way of expressing an idea: "Washington would set a precedent."
George Washington’s presidency set many important precedents, meaning things that he did would be copied by future presidents.
First, there was a huge debate over what we should call the president. Washington wanted to be called “His Excellency” but congress eventually approved “Mr. President” which is how one would address the president even today.
Washington also introduced the concept of the presidential cabinet, which he formed with his secretaries as an advisory board. The exact shape of this body was not outlined by the constitution, and Washington’s choices were repeated after he resigned.
His two-term limit was one that almost every president except Franklin Roosevelt, and he was the first to reestablish diplomatic relations with Britain, a country who is our strongest ally to date.
Washington also established the tradition of farewell addresses, where the president gives one final speech upon exiting office.
All of these were established by Washington.