You can leave the server components on the existing server. The only thing which you need to install on the new server is the client component of the tool. This would be what ever software is normally installed on the users workstation. If it’s a web based application then all that the users will need access to is Internet Explorer.
However, if the applications are not management apps or are client/server apps you may need to install the applications and either configure them or create ODBC connections to the other system.