The son of former Liverpool and England midfielder Jamie Redknapp, Beau made his debut as a second-half substitute in Brentford U21s' 1-0 win against Bristol City.
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Michel Boni scored the only goal of the game with his 11th of the season in the first half.
First year scholar Redknapp made his Under-21s debut coming off the bench with just over 15 minutes to play.
The teenage midfielder was snapped up after successful trials in the summer, he previously played for Sutton United.