If you want to take the approach of the Android model, you can run the app in a Sandbox. Alternatively, or in addition to that, you can also use
DAC (Discretionary Access Controls); or, perhaps, use separate unprivileged users to further isolate specific items, which makes it easier to put in place restrictions without affecting other users and/or the system; same thing with groups: create a group with specific permissions and add a user to that group.
The android approach is to run the apps within the sandbox, and allow the application to perform certain functions outside of that sandbox. There's a clear distinction between that and the idea of limiting the operations of a process "at the kernel level".
This answer is not, by far, a complete list of tools or use-cases available for such scenarios. For example, using the firewall is another obvious method to limit network access both inbound and outbound; the kernel itself has a number of items that can be enabled/disabled, depending on how it was built or via the
sysctl tool, for example. However, for the most part, this would affect the entire system, rather than just one application.
If you're concerned that an application might be unsafe, don't run it. Alternatively, you can run it in a virtual machine or, to some extent, as a docker container. The latter of those, however, should be carefully configured.
Lastly, examine what the application does from within the source code or find info about it from those who've already done so. Ultimately, you should know what you install and try to adhere to using the official repositories of the Linux distribution.