The Alexander Technique uses your movement (and postures) as a framework to enhance awareness and influence over the connection between thought and physical action.
With skill, you learn to use conscious intention as a way to create a positive change in your coordination; towards more ease in movement.
Students most often use their everyday movements (or utilitarian movement) as the main 'framework' to apply the technique to. This is great, because for the majority of your day we're usually just running the same old patterns of movement, posture (and behaviour); so to make even a small consistent change in everyday movement can really add up in your favour.
That said, the times when I've made the biggest leaps in my practice (and thus improvements in how I feel and move) have been when I also applied the Alexander Technique to more physically dynamic movements such as running, swimming, various types of exercise such as body weight training or yoga, hiking, sports, etc.. Usually for about 3-6 focused months for a single activity at a time.
Often, I find students shy away from applying the Alexander Technique to more dynamic activities for fear of 'doing it wrong'; but in doing so they miss out on the opportunity to discover how to 'do it right'. If done with learning and Alexander Technique principles as the primary focus, then 'the bigger the risk, the bigger the reward' seems to apply.
The Alexander Technique was created with movement in mind, and is designed so that all your movements and activities become a playground for self-understanding, exploration, and development.
So what do you want to apply it to?
What movements are you going to grow your practice and self through?