Hello and welcome to the forum. First you should know that your tree is not a Zelkova it is a Chinese Elm. It is not uncommon that this species is misidentified, presumably to circumvent a restriction on the importation of Ulmus.
Here is a side by side of Zelkova and Chinese Elm.
The Zelkova is on the left. A US quarter Dollar is about 24MM
Chinese Elms also have some variation in leaf shape, here are some examples.
I agree with Toms likely Diagnosis regarding low light and poor drainage. I would not however place it outside just yet. Once the weather warms it should go outside if you have that option. I grow Chinese Elms and manage the, for the most part, as deciduous trees. This means allowing them a dormant period over the winter.
Chinese Elms have a wide distribution and are actually considered sub-tropical. Some do keep them indoors but this requires a greater effort on the part of the grower, far easier to keep them outside.
Here are two articles that should clear this up a little.