I have a Linux webserver with TCL 8.3 installed, and I need to upgrade to TCL 8.4 in order to install Eggdrop. I have installation instructions for TCL 8.4, but do I need to uninstall 8.3 first?

I have shell access to the server, and a very rudimentary knowledge of Linux. Any advice you can offer is appreciated.

Looks pretty straight forward, I think the installer will walk you through it.Is this the one you are talking about;
The install is this;

The download is a tar-gzipped archive. 
To extract, enter the following command at the shell prompt:
gtar zxf /path/to/ActiveTcl-download.tar.gz

In the directory where you extracted the archive, run the install.sh installer
script, which will automatically select between the GUI or text-based installer
depending on your system configuration. After installation, make sure that the
directory containing the installed executables (ActiveTcl/bin) is included in 
your PATH variable.