Welcome aboard buddy!Planning on leaving it in this pot for a few more years to thicken up.
There's plenty to make comment about but just a couple to start with:
Even though you say it looks healthy I think this tree looks quite weak, assuming this is a summer photo (location in the world is important for context). Chinese elms should be dark green with masses of leaves in summer when well cared for.
Lower branches appear very weak. Probably lack of fertiliser? Probably because the top has been allowed to grow too strong, possibly lack of light to lower branches. Any or all of those could be causing the yellow leaves you mention. If those conditions continue it is very likely the lower branches could die completely.
Branches on one side appear stronger and healthier than the other. Generally that's a sign the tree has uneven access to light. To keep a bonsai healthy on all sides it should be turned every week or so that all branches get equal light.
Looking at the soil it appears full of roots. Do you know when the last re-pot was? Root bound trees also tend to be less vigorous so that may also be impacting on general health, yellow leaves and declining lower branches.
You have not included your location in your profile so advice tailored to your climate will be difficult.
Welcome aboard buddy!
where did you get that info from? To leave the tree in pot to thicken it up?
Nebari is quite poor, imo. You have one major root coming straight at the viewer, with small roots around. The soil looks to be very organic heavy, possibly staying too wet. I would repot next spring and do major root work #1.
My next thought is that the tree has very little taper in the trunk. There is mostly a single caliper going to top of the tree. I would look at chopping back at some point and rebuilding the top. It wont hurt because:
The top is very overgrown. Apex needs to be cleaned up if left as is.
Some nice starter material though. I agree with Shibui.
it does need some fresh potting mix and more room for new roots
Now is not the right time to be repotting or pruning roots so leave that till next spring but I think it does need some fresh potting mix and more room for new roots (maybe your nursery knows less about bonsai than they think?) I find that trees really respond after root pruning unlike most assume it will set them back.
In the meantime please feed your bonsai regularly. Aim for every 2 - 3 weeks for liquid feed and occasional slow release application through summer.
It does look like it was shaded far too much but that means the leaves are accustomed to low light. Straight into sun would probably mean sunburn just like us. Gradual introduction into more sun will allow the leaves to build up resistance to UV. More sun means more water so you will need to find a balance between enough sun and ability to water. Root bound can make it more difficult for water to penetrate so extra care with pot bound trees like this. In the meantime please rotate the tree 180 degrees every week so all sides get equal light to build strength. My impression from the photos are that some lower branches are close to the critical stage of giving up for lack f light.
Some pruning in the apex would also redirect some energy to saving those lower branches. Looks like there's way to much up there and probably also far longer than it needs so well overdue for some thinning and shortening..
Hi @connorc. I live in Yorkshire and here's my Chinese elm I snapped 2 or 3 days ago so you can compare how compact the growth can get with proper light, pruning, soil mix and fertilizer. This is the kind of growth you're shooting for eventually. It stays out on the benches in full sun all year, very occasionally if it goes below - 5C it will go in an unheated garage and then straight back out again asap. Good luck with your tree - it's a fascinating hobby.