This is EXCEPTIONALLY important.
Not following through diminishes the effectiveness of a redirect and correction efforts and undermines efforts to establish and maintain expectations for behaviour. Following through has advantages:
It clearly establishes that you mean what you say.
It models assertive behaviour in face of a threat.
It models morally courageous behaviour.
This strategy requires directly confronting the offending student, it takes considerable confidence to ‘hold firm’ in the face of protests and even threats from the student, and it can be embarrassing as the implementation of the strategy is invariably done in full view of the other students in the class. It is understandable that teachers will feel nervous and anxious about following through on a consequence. It is very important that these feelings are not conveyed to students. You must look and act confident and in control, even when your emotions are telling you something different.
It is important not to go from a mild redirect to a more confrontational response quickly, prematurely or inappropriately excluding a student form the classroom eg office referral can have a negative impact on the relationship between teacher and student.
Reference links.