[Old Pedant]

In Java, variables only have scope between the { and } where they are declared.

Since you code

       	try {
             int guess = scan.nextInt();
       	}

that variable is not accessible outside the try block.

The solution is easy (and common!)

public static int guess(){
    Scanner scan = new Scanner(System.in);
    int guess;
    try {
        guess = scan.nextInt();
    }
    catch (InputMismatchException err) {
        System.out.println("Your entry is not an integer between 1 and 100");
        Guess.guess();  // if this is a recursive call, I think it's a bad idea
    }
    return guess;
}