Alarm clock subclass of a clock
I have refactored some of your code, please note that I am ignoring pre-existing libraries since I assume there's a particular reason (educational or otherwise) behind implementing Clock, tick, etc. this way on your own.
class Clock:
class Clock:
    def __init__(self, hours: int, minutes: int, seconds: int):
        self.hours = self.normalize_time_in_range(hours, 0, 23)
        self.minutes = self.normalize_time_in_range(minutes, 0, 59)
        self.seconds = self.normalize_time_in_range(seconds, 0, 59)

    @staticmethod
    def normalize_time_in_range(value: int, lower_bound: int, upper_bound: int) -&gt; int:
        if value &lt; lower_bound:
            return lower_bound
        elif value &gt; upper_bound:
            return upper_bound
        else:
            return value

    def start_ticking(self):
        while True:
            self.tick()

    def tick(self):
        print(f&quot;{str(self.hours).zfill(2)}:{str(self.minutes).zfill(2)}:{str(self.seconds).zfill(2)}&quot;)
        self.seconds += 1
        time.sleep(1)
        if self.seconds == 60:
            self.seconds = 0
            self.minutes += 1
            if self.minutes == 60:
                self.minutes = 0
                self.hours += 1
                if self.hours == 24:
                    self.hours = 0


normalize_value_in_range: Notice you have a lot of duplicated logic in set_time and set_alarm. Most of the logic can be extracted to this more generic implementation.
start_ticking and tick: In your case I found it useful to seperate the loop from the actual tick logic so you can change the loop conditions in subclasses while reusing tick. You will see why this is useful in AlarmClock.
Type annotations: As you can see in the method heads I added some type hints to the newly added methods. This is generally a good idea in regards to documenting your code for yourself and others.

class AlarmClock:
class AlarmClock(Clock):
    def __init__(self, hours, minutes, seconds, alarm_hr, alarm_min, alarm_sec):
        super().__init__(hours, minutes, seconds)

        self.alarm_hr = self.normalize_value_in_range(alarm_hr, 0, 23)
        self.alarm_min = self.normalize_value_in_range(alarm_min, 0, 59)
        self.alarm_sec = self.normalize_value_in_range(alarm_sec, 0, 59)

        self.ticking = False

    def start_ticking(self):
        self.ticking = True
        while self.ticking:
            self.tick()

    def tick(self):
        super().tick()
        if self.hours == self.alarm_hr and self.minutes == self.alarm_min and self.seconds == self.alarm_sec:
            print(&quot;ALARM ALARM ALARM ALARM ALARM!!!!&quot;)
            self.ticking = False


normalize_value_in_range: We can now reuse this method to set our alarm time as well.
start_ticking and tick: Since we seperated the loop from the actual tick we can use Clock.tick() in our AlarmClock without the need for duplicate code. Adding the attribute self.ticking to AlarmClock allows us to break out of the loop across methods. The reason we could not reuse tick() before was because it contained the infinite while True loop, thereby not allowing us to intercept when the alarm_time is reached.

class Time:
Lastly, I would suggest seperating time logic from clock logic. This makes the clocks more concise and allows you to extend the functionality of the Time class as needed. You could also say it allows the clocks to focus on their main functionality. Again, I am ignoring the existence of libraries for this task, since I presume you want to implement the entire logic on your own. Specialized libraries like datetime are worth looking into since they provide a lot of comfortable functionality. One implementation might be the following:
class Time:
    def __init__(self, hours: int, minutes: int, seconds: int):
        self.hours = self.normalize_value_in_range(hours, 0, 23)
        self.minutes = self.normalize_value_in_range(minutes, 0, 59)
        self.seconds = self.normalize_value_in_range(seconds, 0, 59)

    @staticmethod
    def normalize_value_in_range(value: int, lower_bound: int, upper_bound: int) -&gt; int:
        if value &lt; lower_bound:
            return lower_bound
        elif value &gt; upper_bound:
            return upper_bound
        else:
            return value

    def increment(self):
        self.seconds += 1
        if self.seconds == 60:
            self.seconds = 0
            self.minutes += 1
            if self.minutes == 60:
                self.minutes = 0
                self.hours += 1
                if self.hours == 24:
                    self.hours = 0

    def __eq__(self, other):
        return self.hours == other.hours and self.minutes == other.minutes and self.seconds == other.seconds

    def __str__(self):
        return f&quot;{str(self.hours).zfill(2)}:{str(self.minutes).zfill(2)}:{str(self.seconds).zfill(2)}&quot;


class Clock:
    def __init__(self, hours: int, minutes: int, seconds: int):
        self.time = Time(hours, minutes, seconds)

    def start_ticking(self):
        while True:
            self.tick()

    def tick(self):
        print(self.time)
        self.time.increment()
        time.sleep(1)


class AlarmClock(Clock):
    def __init__(self, hours, minutes, seconds, alarm_hr, alarm_min, alarm_sec):
        super().__init__(hours, minutes, seconds)
        self.alarm_time = Time(alarm_hr, alarm_min, alarm_sec)

        self.ticking = False

    def start_ticking(self):
        self.ticking = True
        while self.ticking:
            self.tick()

    def tick(self):
        super().tick()
        if self.time == self.alarm_time:
            print(&quot;ALARM ALARM ALARM ALARM ALARM!!!!&quot;)
            self.ticking = False