ElasticSteel Paul shows a few techniques to increase the height of the side kick. (Focus on the supporting leg)High side kick to the rescue of high side kick
Work the techniques in the order shown. Master each exercise in progression. Do start the later part of the video which involves stretching and strengthning in extended length of the muscles, before strengthing and conditioning.
This also helps for a
high roundhouse kick and for a
high hook kick.
Korean Martial Arts and other martial arts as well.