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Usually a coach on his first arrival to a new team is not given all of the complete confidence, he has to stay awhile through a season or halfway a season and his performance will gradually help him win the confidence of the fans and the Management of the team. The management of Leverkusen wanting their team at the top is a normal thing every other management will want with their team so I believe they have understood Ten Hag has some abilities that will help them maintain that status not minding his Manchester United records because they are obviously two different leagues and teams.
Ten Hag must fight to win over the fans, and that can only be done by leading Leverkusen to consistent victories. Meanwhile, regarding Ten Hag appointment as the new manager, Leverkusen management must have conducted a thorough evaluation of his capabilities. They wouldn't carelessly appoint a new manager, they clearly choose a manager who shares their vision. However, Ten Hag poor reputation with Manchester United is always the main narrative, maybe in Leverkusen, Ten Hag performance will be better.