As of March 2022, under macOS Monterey 12.2.1, I had to use a different PATH change to reach pip:

export PATH="$PATH:/Users/<username>/Library/Python/3.8/bin"

Notes:

1. My python installation is not at /Library/ but rather at ~/Library/, possibly because it arrived via brew - or that Monterey uses a different location.
2. $PATH does not seem to tolerate ~/ - so one rather has to use /Users/<username>/... in at least this case.
3. I think it's better to append rather than to prepend the updated path, because by default one might want/expect the system's main paths (/usr/bin etc.) to take precedence. On the other hand, installing e.g. python to those main paths will also take precedence over any python setup that depends on the updated path and could therefore damage it. Choose your poison.
4. This answer is not the same as the currently-top answer because (i) the required path is different for me and (ii) the OS version is different.

You need to add to your .bash_profile or .zshrc in your system root directory:

export PATH=/Library/Frameworks/Python.framework/Versions/3.9/bin:$PATH

If you are on a Raspberry Pi (Raspbian OS) then do the following:

nano /home/pi/.profile

At the end of the file add:

# set PATH to pip
PATH="$HOME/pi/.local/bin:$PATH"

Ctrl+X, Y, Enter <-- to save changes on the .profile file

Then reboot your Raspberry Pi to apply changes.

You can check now with pip --version

You are getting this error because of the absence of the location that pip is installed from your PATH.

You need add:

export PATH="$PATH:/Library/Frameworks/Python.framework/Versions/3.8/bin"

to the end of your .bash_profile, like @hoefling commented.