Generally speaking, you should be able to compile the new version without having to worry about the old one. That being said, compiling and installing from source won't necessarily remove previous versions of the software.
Additionally, some applications have 'make uninstall' enabled. However, that would require that you kept the source directory around after the initial compile and installation of the software. If that's the case, you might want to do a 'make uninstall' from the directory that the source code lies in.
As a general rule, though, unless the installation instructions that came with the updated app specifically state that all previous versions must be removed first, I don't normally worry about it.