You may have installed TeX Live in one of two fundamentally different ways. The way to install and update packages depends on which way you got your installation.
First, you may have gotten a TeX installation that was based on TeX Live but was packaged for your operating system. For instance, the free GNU/Linux distributions, and the distributions from Red Hat, Debian, Ubuntu, SUSE, etc., all make TeX installations derived from TeX Live available through their normal packaging system (rpm, apt-get, yum, etc.). If this is how you got your TeX, the timing and content of updates is entirely up to your operating system provider—contact them with any and all questions.
By the way, native TeX Live, which is typically installed under /usr/local, can happily coexist with a TeX from your operating system, each with their own completely independent trees and programs. (Do not try to merge them!) So you can install native TeX Live if your vendor is not keeping up.
The other case is that you installed the “native” TeX Live, e.g., from the DVD or over the net. Here, the first thing to try, both to install new packages and to update already installed ones, is to run (on a command line/system prompt) the command tlmgr update --all (tlmgr is the command name of the TeX Live package manager). To see what would be done before doing it, run tlmgr update --list.
If that doesn't get the material that you want, then here is one possibility. When you installed your native version of TeX Live, the default was to include everything available for your platform. If you accepted this default, called scheme-full, then the above command gets you the freshest version of everything available. However, if you chose a smaller scheme than the default, then you will get only what is included in that scheme. Likewise, if you have manually removed collections or packages (terminology explanation), then those packages will not be automatically updated. In these cases, to manually (re)install a package, run tlmgr install pkgname.
If you used scheme-full, and you still didn't get the
material you were expecting, here are two other possibilities:
1) the TeX Live developers have not yet made the update.
This is usually done within a day or two of the upload to CTAN, but
occasionally it can take longer.
2) the package may not be available under a free software license,
among other issues, in which case it cannot be included in TeX Live (the package contribution page explains).
More information is in the full tlmgr documentation.
Yet one more possibility for a package failing to be installed is that it is not in TeX Live; for instance, if it is non-free. The tlcontrib repository includes additional packages that can be legally distributed, but not included in TeX Live for whatever reason.
Our packages are signed with GnuPG. For convenience, you can get gpg packages for TL on Windows and Mac from the third-party tlgpg repository.
Native TL updates ultimately come from a directory named tlnet (on CTAN). An archive for tlnet is available, with daily updates since September 2019, and the final yearly release going back about ten years.
The additional repositories above (and plenty more) are hosted on the texlive.info server, along with several other archives and repositories, currently maintained by Norbert Preining.
To explain the terms schemes, collections, and packages used above: the general idea of native TL installation is to choose one of the available top-level schemes, each of which is defined as a set of collections and packages. A collection is a set of packages, and a package is what contains actual files. Each package is in exactly one collection, no more and no less.
If you have questions or suggestions, please email tex-live@tug.org.