I will understand the players they have prepare how they perform because Erik ten Hag job is to improve the effort and experience then we have to decide whether the team play well on the field. If Leverkusen defense and their strength are such that they beat every team by a certain goal in every match then we can give them a clear lead in the league. This will show their strength their power and their effort to win the title. What kind of idea is it if they get a better player after lose them. If they adopt a player who has more strength and effort and tries to score more goal in every match it would be better for them to lose them. But I would say that they should replace them with some good player who can bring them to the first position. This will give them a lot of advantage which will increase their strength and their hope a lot.
Ten Hag will.do everything in is power to do better than the formal coach they want the club to do better because everything is already looking at stake because if the club those not do well then it's going be him at the receiving end. So at all cost improving the club will be the only thing that he will have to thinks of, and Leverkusen is not that stressful because the amount of things is going to put in, and since the day the job is accepted he would have know what he needs to improve both the attack and the defence of the club.
I suspect you wanted to writer "former" coach instead of "formal" coach, but anyway, expecting ten Hag to do better than the former coach, namely Xabi Alonso, is utter nonsense. Alonso won the Bundesliga title without losing a single game that season, the DFB Pokal, reached the Europa League final and then became vice champion last year. What do you think the Leverkusen bosses want ten Hag to do?
The competition with Bayer Leverkusen is no less because the bosses do expect Leverkusen to have a say in the title race. I don't think Manchester United really believes in a chance to win the Premier League anytime soon.