While having history available with the simple use of the up arrow is a convenience feature common to most linux builds it can come with some risk. One such risk is when you have inadvertently typed a password instead of a command, or had to pipe credentials into a command.
Thankfully, you can clear the entire history with a variety of methods, the most common are below but others are available in the references.
history -c && history -w
cat /dev/null > ~/.bash_history && history -c && exit