How to install Homebrew without Command Line Tools if already have Xcode
Apple's website for downloading developer tools says that &quot;If you use Xcode, these tools are already embedded in the IDE.&quot;
So you shouldn't need to install them again.
But, as mentioned in the commments: it's a 460 Mb download. If you don't have space for that, you're not going to have space for HomeBrew, or any of the things it installs.