TL;DR: printf 'e[3J'
Depending on your terminal, simple clear might clean only the visible portion of the screen, leaving scrollback intact.
Sometimes it might be not what you want, and then printf '\e[3J' might help you.
Note that sometimes this command might clean only scrollback, and you might want to have both!
Source: stackoverflow.
A good header for a script that produces a lot of output then looks like this:
clear
printf '\e[3J'
set -ex
It first clears visible screen and scrollback, and then enables failing on error and echoing lines to be executed