How to create depth in this rectangular zentangle drawing?
You can use shading.
As light naturally comes from above, the most logical approach to create a sense of depth is to add shadows to receding areas based on an imaginary light source straight above it, like this:

Also note that the frame you are referring to has a lot of relief that similarly obscures and catches light, which has a huge effect on a sense of 3-dimensionality.
This you can likewise easily simulate by shading the decorative patterns, like this:

Because your drawing seems to have been done in pen, you can - depending on the paper - add these shadows using a large variety of mediums, from pencils to paints, with charcoal being the easiest and quickest way.