Moving web hosting and domain with custom gmail email

I have read Ian Lloyd’s HTML and CSS book and thought someone on this forum could maybe help with my questions. I’m a student so this is my first time dealing with web hosting and domain name transfers.
I’m creating a website for a company which is due to go live in the next week or so. The company already have a website created and hosted on weebly but I am going to move the domain name and web hosting to another company. I think I am comfortable with doing this but my main issue is that the company have a custom email address from Gmail using their domain name. This email is important to the company so they can’t afford to lose any mail or not be able to receive any email. Does anyone know if moving the domain and hosting would affect this email account? I heard something about transferring the domain but not changing any of the nameservers. Can anyone explain what this means?

Many Thanks

Are the domain name and hosting supplied by different companies?
Typically, a domain name will be held and paid for at a domain registrar. Within the domain control panel will be settings for nameservers and DNS.
The domain will likely be using the registrars nameservers. Even if you discontinue using any hosting supplied by the same company, you can still leave the domain there using their nameserver, and just update the DNS records to point the website at the new hosting. A particular part of the DNS records for the domain called MX records decide which mail servers (in your case google mail servers) email gets directed towards. As long as you don’t touch the MX records or change nameservers, the email should be safe.

Thanks for your reply.
The domain was purchased through weebly but according to it is supplied by Weebly provide the hosting. So when transferring the domain name and hosting if I choose not to change nameservers this should be ok? What difference does this have to changing nameservers?

I had a look on the weebly site - this should allow you to host elsewhere while retaining the domain registration at weebly and without changing nameservers

Thats great. Thank you. I really appreciate the help.