TLDR:
asdf install elixir latest
asdf global elixir latest
Or in your specific case: asdf global elixir 1.14.0-rc.1-otp-25
See the Set a Version section of the asdf docs:
6. Set a Version
asdf performs a version lookup of a tool in all .tool-versions
files from the current working directory up to the $HOME directory.
The lookup occurs just-in-time when you execute a tool that asdf
manages.
::: warning Without a version listed for a tool execution of the tool
will error. asdf current will show you the tool & version
resolution, or absence of, from your current directory so you can
observe which tools will fail to execute. :::
Global
Global defaults are managed in $HOME/.tool-versions. Set a global
version with:
asdf global nodejs latest
$HOME/.tool-versions will then look like:
nodejs 16.5.0
Some OSs already have tools installed that are managed by the system
and not asdf, python is a common example. You need to tell asdf
to pass the management back to the system. The Versions reference
section will guide you.
Local
Local versions are defined in the $PWD/.tool-versions file (your
current working directory). Usually, this will be the Git repository
for a project. When in your desired directory execute:
asdf local nodejs latest
$PWD/.tool-versions will then look like:
nodejs 16.5.0
Using Existing Tool Version Files
asdf supports the migration from existing version files from other
version managers. Eg: .ruby-version for the case of rbenv. This is
supported on a per-plugin basis.
asdf-nodejs supports this
via both .nvmrc and .node-version files. To enable this, add the
following to your asdf configuration file $HOME/.asdfrc:
legacy_version_file = yes
See the configuration reference page for
more config options.