Delete PPA after install the software?

Adding a PPA to our sources give us the advantage to install newer application versions that did not yet find their way into the official repositories.

However by doing so we may also introduce instabilities from not yet fully tested releases.

In case we keep the PPA active this will also automatically install any software upgrade that was provides from this PPA. By this new bugs may be introduced. It is therefore good practice to inactivate a PPA after we had successfully installed a package we are happy with.

This can be done by just unticking a PPA from Software & Updates. By this we can easily activate it again in case we want to upgrade later:

Only if we are sure that we always want a fresh new release of any package, and the PPA will not provide updates for other packages we may keep it active.

Few PPAs will also provide security updates. In this case we also may want to keep the PPA active. However in general having packages from a PPA is not without risk.

If you delete the PPA then you'll still able to use the application normally since the PPA is just a software resource nothing more._{Read More}

But, you may use the PPA for next release, updates ,security , bug fix, patches, etc...

So, it's better not to delete the PPA if you want to be up to date with these software

Is it safe to delete the PPA after successful installation of the package?

Depending on what you consider "safe". Yes, you can delete any software repository from your sources.list you wouldn't notice. But, you also will be unable to upgrade the packages from that repository, which may offer bugfixes or security patches.

It is recommended that unless you have a very good reason, you keep the repositories on your sources.list (apt 1.1.10+ changes the strategy to update package lists, which improves performance) and allow upgrades. If you want to keep a package on a specific version, you may instead prevent upgrades of that specific package until you are ready to upgrade it, without affecting other packages that the repository provides.

Note that it is normally unnecessary to remove a line of the sources.list since you can comment it out (# at the start of the line), which prevents you from forgetting from what repository you installed a specific package.

PPA's maintainers are known for not following the packaging guide thoughtfully which may cause problems. If you are able to get the package through Ubuntu's own repositories, you are less risky of running into problems.