Is It Possible to Clench Your Teeth in an Effort to Make Jaw Muscles Bigger and Achieve This?

The lower cheek can be wider over time as the muscles hypertrophy related to chronic clenching. The masseter muscles are often seen to enlarge with chronic clenching and some patients see doctors for the off-label use of Botox injections to thin out this mass.

The information provided in Dr. Shelton's answer is for educational purposes only and is not intended to constitute medical advice.  The information provided should not be relied upon as a substitute for consultations with a qualified health professional who may be familiar with your individual medical needs.

Just like any muscle on your body, if you frequently contract your muscles in the jaw then they will get stronger and thus more prominent.

I think it is possible that by clenching your jaw more that you can see the muscle get bigger.  The main jaw muscle (the masseter) can get bigger by working it out, just as the arm muscle (bicep), for example, would if you worked it out more.  I wouldn't necessarily recommend clenching the jaw a lot though, as this can lead to other potential problems, such as issues with TMJ (the jaw joint).    

We know that clenching your teeth over time will build up the masseter muscles in the area. If they are of concern to you, experienced injectors can use toxins to minimize this – so I would consult a board-certified dermatologist or plastic surgeon.

The muscles of the jaw are just like other skeletal muscles and will grow with repeated flexing.  Clenching the jaw flexes those muscles.