Managing someone who knows more than you do
Someone on your team has been doing this work for twenty years. You have been doing it for four, and you are their manager. In any conversation about the detail, they are right more often than you are, and you both know it.
So you overprepare for your one to ones. You explain things they understood long before you arrived. Or you go the other way and stop asking about their work at all, which they notice faster than you would like.
Neither of those is a way of managing them. Both are ways of managing your own discomfort.
Where the discomfort comes from
Most of us pick up an idea early that authority is earned by being the most capable person present. You probably came by it honestly. You were promoted for knowing, and it worked, right up until the job changed underneath you.
Nobody tells you that the source of your authority is supposed to change with it. So you keep reaching for the old one, and it keeps not being there.
Think about the leaders you have respected most. Were they the ones with the deepest technical knowledge? Or the ones who made it possible for knowledgeable people to get something done?
Bluffing is the one thing they will not forgive
Your expert can work happily for a manager who knows less than they do. They have probably had several. What they cannot work with is a manager who pretends.
They can tell immediately. You nod along to something you did not follow, and they watch it land. After that, everything you say gets weighed for whether you mean it.
So say you did not follow it. Ask them to go again, more slowly. What did that cost you? Nothing you had in the first place.
Ask the questions you are qualified to ask
You do not need their expertise to be useful to them. There is a whole set of questions you can ask without knowing the subject, and they are often the ones nobody has bothered to ask.
What would have to be true for this to be the wrong call? What are we assuming that nobody has checked? If it takes twice as long as you think, what happens to everything else we promised?
Experts are rarely short of answers. They are short of people who make them show their working. You can do that on your first day, and the good ones enjoy it more than you would expect.
Take the part of the job they do not want
Ask what they need from you and you will get a polite non-answer. Watch instead.
The expert on your team is usually being worn down by things that have nothing to do with their expertise. Requests that land on them because everyone knows they will sort it out. A decision that has sat unmade for two months while they build around the gap.
That work belongs to you. Not because it is beneath them, but because you are the one who can end it. You can go to the other manager yourself. You can say no on their behalf, and you can force the decision that has been sitting there, or make it and carry it.
Do that twice and the question of who knows more stops being interesting to either of you.
When you decide against them
It will happen. They will be right on the merits and you will still go the other way, because of something they are not carrying. A promise made somewhere else. A risk with your name on it rather than theirs.
Do not dress that up as a technical argument. You will lose it, and you will deserve to.
Say it straight instead. Their analysis is sound, you are going a different way, and here is what is driving that. Then tell them what would change your mind, and mean it.
Most experts do not need to win. They need to know the decision was made by someone who understood what they said. You can give them that without knowing more than they do.
None of this asks you to close the gap between what they know and what you know. That gap is the reason they are worth having, and if it ever closes it will probably be because they have gone somewhere else. Your job is the conditions their work happens in. That has never once required being the cleverest person on the team.