If you wish to add output from a command to a file rather than replace it, double the right angled bracket to >>:

$ printf 'First command\n' > file
$ printf 'Second command\n' >> file
$ cat file
First command
Second command

The file doesn't need to exist already for this to work; the >> operator will create it for you, just like the > operator will.

This is a useful syntax for appending to log files, describing the output of your script as you go:

#!/bin/bash
printf 'Starting script\n' >> log
printf 'Creating test directory\n' >> log
mkdir test || exit
printf 'Changing into test directory\n' >> log
cd test || exit
printf 'Writing current date\n' >> log
date > date || exit