I really loved the kalarm Version 2.10.10-ak. When I install kalarm from the synaptic repository I get the version 2.11.4-5ak which I don't like. Is there any way to install the older version on to another computer?

You would have to find a distribution which provided a package for the the older version. It may not be possible to install an older version of KAlarm on a system which provides the newer version, because of the fact that the two versions use incompatible KDE libraries. Unless the distro allows both KDE 4 and KDE 5 libraries to be installed alongside each other, it wouldn't work.

The other alternative would be to use an older version of your distro, or you could use another distro - Debian stable (jessie), for example.