Hackerrank problem: Climbing the Leaderboard (Java)
I have some suggestions to make the code cleaner, not faster.
Always try to pass the size of the maximum size to the Collection / Map when known
The ArrayList has a default size of 10 elements, if you have more elements, the list will have to resize its internal pool. By setting the size, you can prevent the resize and make your code faster.
//[...]
int totalPlayers = scanner.nextInt();
ArrayList&lt;Integer&gt; playerScores = new ArrayList&lt;&gt;(totalPlayers);
//[...]
int aliceTotalScores = scanner.nextInt();
ArrayList&lt;Integer&gt; aliceScores = new ArrayList&lt;&gt;(aliceTotalScores);
//[...]

Always use the base class / interface in the left part of the variable when possible
By setting the java.util.List interface in the variable part, this could make the code more refactorable in the future, since you could easily change the list type without changing everything (inheritance).
Before
 ArrayList&lt;Integer&gt; playerScores = new ArrayList&lt;&gt;(totalPlayers);

After
 List&lt;Integer&gt; playerScores = new ArrayList&lt;&gt;(totalPlayers);

Replace the for loop with an enhanced 'for' loop
In your code, you don’t actually need the index provided by the loop, you can the enhanced version.
Before
for (int i = 0; i &lt; aliceTotalScores; i++) {
   finalScores.add(aliceScores.get(i));
   finalScores.sort(Collections.reverseOrder());
   Set&lt;Integer&gt; set = new LinkedHashSet&lt;&gt;(finalScores);
   finalScores.clear();
   finalScores.addAll(set);
   System.out.println(finalScores.indexOf(aliceScores.get(i)) + 1);
}

After
for (Integer aliceScore : aliceScores) {
   finalScores.add(aliceScore);
   finalScores.sort(Collections.reverseOrder());
   Set&lt;Integer&gt; set = new LinkedHashSet&lt;&gt;(finalScores);
   finalScores.clear();
   finalScores.addAll(set);
   System.out.println(finalScores.indexOf(aliceScore) + 1);
}

Extract some of the logic to methods.
To remove some of the code of the main method, you could move both list instantiation (playerScores &amp; aliceScores) to methods. Since the logic is similar, you could make only one method to read the inputs to a list and reuse the same for both cases.
public static void main(String[] args) {
   List&lt;Integer&gt; playerScores = getPlayerScores(scanner);
   List&lt;Integer&gt; aliceScores = getAliceScores(scanner);
}

private static List&lt;Integer&gt; getAliceScores(Scanner scanner) {
   return getIntegers(scanner);
}

private static List&lt;Integer&gt; getPlayerScores(Scanner scanner) {
   return getIntegers(scanner);
}


private static List&lt;Integer&gt; getIntegers(Scanner scanner) {
   int size = scanner.nextInt();
   List&lt;Integer&gt; integers = new ArrayList&lt;&gt;(size);
   for (int i = 0; i &lt; size; i++) {
      integers.add(scanner.nextInt());
   }
   return integers;
}


or
public static void main(String[] args) {
   List&lt;Integer&gt; playerScores = getIntegers(scanner);
   List&lt;Integer&gt; aliceScores = getIntegers(scanner);
}

private static List&lt;Integer&gt; getIntegers(Scanner scanner) {
   int size = scanner.nextInt();
   List&lt;Integer&gt; integers = new ArrayList&lt;&gt;(size);
   for (int i = 0; i &lt; size; i++) {
      integers.add(scanner.nextInt());
   }
   return integers;
}


Refactored code
public static void main(String[] args) {
   Scanner scanner = new Scanner(System.in);
   List&lt;Integer&gt; playerScores = getPlayerScores(scanner);
   List&lt;Integer&gt; aliceScores = getAliceScores(scanner);
   List&lt;Integer&gt; finalScores = new ArrayList&lt;&gt;(playerScores);

   for (Integer aliceScore : aliceScores) {
      finalScores.add(aliceScore);
      finalScores.sort(Collections.reverseOrder());
      Set&lt;Integer&gt; set = new LinkedHashSet&lt;&gt;(finalScores);
      finalScores.clear();
      finalScores.addAll(set);
      System.out.println(finalScores.indexOf(aliceScore) + 1);
   }
}

private static List&lt;Integer&gt; getAliceScores(Scanner scanner) {
   return getIntegers(scanner);
}

private static List&lt;Integer&gt; getPlayerScores(Scanner scanner) {
   return getIntegers(scanner);
}


private static List&lt;Integer&gt; getIntegers(Scanner scanner) {
   int size = scanner.nextInt();
   List&lt;Integer&gt; integers = new ArrayList&lt;&gt;(size);
   for (int i = 0; i &lt; size; i++) {
      integers.add(scanner.nextInt());
   }
   return integers;
}