amazon ec2 - Subdomain using AWS Route 53, load balancer, EC2, Apache

I've tried to follow a few different tutorials on this, but can't quite get it to work.

I have all of my DNS for my domain (example.com) in Route 53. Works fine.

My top level domain (A record) points to my load balancer (AWS) as an alias. This points to an EC2 server and works fine.

I want to add a subdomain (client.example.com), but I'm not quite sure where to add this and what type of records I need. I want this to point to a directory on the same EC2 server as my top level domain (which would have the path example.com/client). I don't want it to redirect, just serve the files from this directory.

Not sure if I need to create a new hosted zone or not, what to put in the zone, what to point it at, and if I need to modify anything on my server (like a rewriterule).

Any direction would be appreciated.