How can I emulsify Beeswax with Aloe Vera Gel?
Aloe vera gel is water based, whereas beeswax is, well, wax-based. As they say, "oil and water don't mix" -- at least, not on their own.

So, the trick is to make them willing to mix. To do this, you need what's called an emulsifier. These are chemicals (natural or synthetic) that have both oily and watery parts to them, and thus are able to make oil and water play nice(r) with one another.  Soap is one well-known, everyday example of an emulsifier; in particular, it's an example of a surfactant.

Anyways, you need an emulsifier. If you're looking to stick with natural products, probably the most readily available option is lecithin, commonly sourced from soy but also available derived from other plants such as sunflower.  While I don't have detailed recommendations, I would melt the beeswax together with lecithin and the aloe vera gel over very low heat, mixing thoroughly, then allowing the blend to cool.  You'll have to experiment until you find a ratio among these that gives the consistency you want in the final product.