Definition from the EU Commission.
“A person who works as an employee or self-employed person in one EU Member State but is recognised as residing in another (neighbouring) EU Member State”.
“If you work in one EU country but live in another and return there daily, or at least once a week, you count as a cross-border commuter under EU law (sometimes called cross-border or frontier worker)”.
From the Withdrawal Agreement.
Issuance of a document identifying frontier workers’ rights
The State of work may require Union citizens and United Kingdom nationals who have rights as frontier workers under this Title to apply for a document certifying that they have such rights under this Title. Such Union citizens and United Kingdom nationals shall have the right to be issued with such a document.