Configure a webserver answering requests for
https://a.site1.example which will return HTTP redirects for any URL and pointing to
DNS wise this means that both names must resolve (through A/AAAA/CNAME records) to the correct servers, the same one or separate ones (your question lacks details)
If you do not want people to see the new URL then the first webserver needs to be configured as an HTTP proxy. This comes with various drawbacks, including performance loss to start with, but again your question lacks specific details.