On Debian-based systems one has two options:

a) Install from Debian testing:

• add testing repo
• pin all packages from Testing, except handbrake*, with negative priority
• and hope installing works without having conflicting dependencies.

b) Build from source:

• Activate the deb-src repos in the sources,
• install build tools: sudo apt install build-essential dpkg-dev
• install the build dependencies of handbrake: sudo apt-get build-dep handbrake,
• download the source archive from their website (or from Debian testing),
• follow their build instructions,
• recommended: build a deb package and install. (see Advice For New Users On Not Breaking Their Debian System and CheckInstall for more advice)