The first official release of biblatex-ext is dated 2018-03-18 and was announced on CTAN on 19th March 2018. TeX live 2017 was frozen around 2 March 2019 (for more on these freezes see Why does TeX Live "require" yearly updates?), so biblatex-ext did not make it to TeX live 2017 and is only available in TeX live 2018 and above.
The recommended way to install biblatex-ext is via a TeX distribution that ships it, so in this case installing TeX live 2018 (probably the vanilla version from TUG if you are using Linux How to install "vanilla" TeXLive on Debian or Ubuntu?) is the way to go. Then biblatex-ext is either installed already or can be installed with tlmgr.
If that is out of the question, you can install the package manually. This is explicitly discouraged, but possible.
The newest version available on CTAN was written for biblatex 3.12 and should not be used with older versions of biblatex that can be found in TeX live 2017 (a regular TeX live 2017 should have biblatex 3.10 at most).
Older releases of biblatex-ext can be found at https://github.com/moewew/biblatex-ext/releases. Versions 0.1 up to 0.5a were all written for biblatex 3.11. They were not tested with older version of biblatex and they will issue a warning if used with an older version, but most things should work with biblatex 3.10.
For TeX live 2017 I would recommend to download v0.5a from https://github.com/moewew/biblatex-ext/releases and follow Method 3 in How do I install an individual package on a Linux system?.