Dreaming of an alarm clock can be a message from your unconscious that you need to be more prudent, that you need more discipline, or that you need to have more willpower.
Hearing an alarm clock in your dream can be a reminder that it is time to do something.
You may have been avoiding taking on an unpleasant task.
A dream that you hear an alarm clock but ignore it and go back to sleep can be a message that something in your life is not as important as you thought it was.
If you are a lucid dreamer, an alarm clock in a dream may be a reminder that you need to wake up.