so you can do 2 things:
- change the nameservers to the new site
- change the A record
So lets say you have server A (where you have your wordpress site right now) and server B (which is the new one).
In namecheap you can control the NameServer that looks something like this:
ns1.serverA.com - ns2.serverA.com
so if you are changing servers, you can update it to
ns1.domainB.com - ns2.domainB.com
those nameservers are giving to you when you get that new server.
The other case is changing the A record, which you are just going to change an IP from namecheap and everything else still the same. For that you need to go to DNS Settings (or advanced DNS settings) and looks for A record, then you just need to update the IP to the new one of the new server and that would be it.
let me know if you have any questions
good luck