we need someone expert which can help transfer site from one server linux/cpanel to another server linux/cpanel
Yeah, your host should do it for you. It's very easy. Even with a full backup, your host will have to restore it for you anyway, so might as well put in a ticket.
Cpanel has a feature where it will transfer the site for you, all you need is ftp details. If you cant do it, pm me
@Master Directory, cPanel -> cPanel transfer would be sufficient to copy on most cases. If home directory is big, it will stream the files form source -> destination without creating an archive.
If you've root access then also you can use wget command and then use cPanel multiple account restore features(I use this when cPanel failed to copy account from other server)
Yeah if you don't know anything about making backups and restoring, I would send in a ticket to your new host and 9 times out of 10, they will do it for you for free.