Beck had joined the Championship club on a season-long deal, but the wing-back failed to make an appearance due to injury.
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The Wales international has now returned to Liverpool where he will continue his injury rehab at Melwood.
Beck, a product of Liverpool's Academy set-up, has appeared three times for the club's senior team to date, having debuted in October 2021.
Before joining Derby, he signed a new, long-term contract with Liverpool.