You would have to download a binary or source+compile to get the newest 7.0.75 instead of 7.0.52 delivered with Ubuntu 14.04
There’s a longer answer about this here:
http://askubuntu.com/questions/403453/how-to-install-latest-version-of-tomcat-on-ubuntu-using-apt
Alternatively you could upgrade your 14.04 to 16.04, but that would only give you 7.0.72

@gencaysahinn

When it comes to Ubuntu, you’re best bet is to deploy new Droplets with Ubuntu 16.04 as 14.04 is nearly EOL (end of life), which means support for it will be dropped. Ubuntu 16.04 is the newest LTS release (Long-Term Support).

In regards to Tomcat, if you need the latest version and the package repositories are not providing it yet, or won’t be, the alternative is indeed, as @hansen mentioned, to compile from source.

If you take a look here:

https://launchpad.net/ubuntu/+source/tomcat7

.. you’ll see that Tomcat 7.0.75-1 is available, though it’s marked as unstable, thus you’d be using it at your own risk if you chose to install it. Only 7.0.72-1 is the latest stable release.