No we are only moving to a new hoster for our current website (eg currentsystem.com) - our current hoster is based in Indonesia and is cheap (good during COVID!), but the hosted websites suffer from some technical SEO issues such as speed, etc.
For our osTicket system we want to move to a new domain on the current hoster (eg from currentsystem.com/osticket TO newdomain.com/osticket). This means migrate the existing osTicket system (files, DBs, etc) to the new domain.
We are staying with the same hoster for osTicket because the DBs are too big to move. Since the users of our osTicket system are our internal staff we are not too concerned with website speed.