ArrayLists and returning null

public static Integer priority(String name) {
        for(int i = 0; i < ALL_TASKS.size(); i++){
          if(ALL_TASKS.get(i).getName().equals(name))
            return ALL_TASKS.get(i).getPriority();
          else
            return null; // but if using Java 8 Option<Task> would be better
        }
    }

This is the example which I would use. It is not tested but it give you idea what create and the way of thinking.

Also in my solution I assume you also create getName() and getPriority() methods for your Task

Try this:

public static Integer priority(String name) {
    for(Task task : ALL_TASKS) {
        if(task.name.equals(name)) {
            return task.priority;
        }
    }
    return null;
}

Or using Stream-API:

public static Integer priority(String name) {
    return ALL_TASKS.stream()
            .filter(task -> task.name.equals(name))
            .map(task -> task.priority)
            .findFirst()
            .orElse(null);
}

The Java Stream API provides a more convenient and efficient approach to iterating and processing elements of a collection.

class Task
{
    public static final ArrayList<Task> ALL_TASKS = new ArrayList<>();

    public static Integer priority(String name)
    {
        List<Task> result = ALL_TASKS.stream().filter(task-> 
                          (task.name.equals(name))).collect(Collectors.toList());
        if(result.isEmpty())
        {
            return null;
        }
        else
        {
            return result.get(0).priority;
        }
    }

    private String name;
    private Integer priority;

    public Task(String name, Integer priority)
    {
        ALL_TASKS.add(this);
        this.name = name;
        this.priority = priority;
    }

    public String toString()
    {
        return "name: " + this.name + "\tpriority: " + this.priority;
    }
}

class Main
{
    public static void main(String[] arguments)
    {
        new Task("Clean", 5);
        new Task("Dishwash", 4);
        new Task("Study", 1);
        System.out.println(Task.priority("Dishwash"));
        System.out.println(Task.priority("Vacuumclean"));
    }

}

An option would be storing your List as a Map instead, using the tasks name as the key

HashMap<String, Task> ALL_TASKS = new HashMap<>();
Task task = ALL_TASKS.get(codeIsIn);
if(task!=null)
{
    Integer priority = task.priority;
}

If a Task consists only of name and priority, it gets even simpler

HashMap<String, Integer> ALL_TASKS = new HashMap<>();
Integer priority = ALL_TASKS.get(codeIsIn);
//null if nonexistent