Updated: Jul 17, 2022
This thread is written in response to one of the most frequently asked questions in Catan: "Do you ever need to activate your Knight when the robber is already resting on the leading player's most productive hex?". Without a doubt, the answer is "Yes, you do.". In fact, there are various cases where you will find it necessary to shoo Robbie regardless of how good his current place is. Before we begin, keep in mind that in the examples we provide, you are not the one leading ahead. Now, let's dissect the topic together!
First and foremost, you might consider activating a Knight to get, secure, or take over 02 Victory Points of the Largest Army. It is particularly urgent when the leader is about to end the game with the Largest Army. And even when their road to victory has nothing related to the Largest Army, you still need to make sure those 02 VPs belong to you for good. Anyways, finishing with more VPs cannot hurt, can it?
Secondly, use your Knight when you have a high chance or are guaranteed to get a specific resource to (once again) get, secure, or take over other types of VPs immediately afterwards. This is usually worth attempting if you are after the Longest Road or a productive VP such as a settlement or a city, but not another development card unless you are certain the game is going to be ended this round.
Next, aside from helping yourself, you can use a Knight to disrupt the opponent's tactic. If the situation is right, stealing a card could break their winning combination of resources in hand. Also, sometimes their hex with the highest production rate cannot help them win right away, but a slightly worse one can (e.g. 05 Sheep on an 8 hex vs 03 Ore on a 10 hex). In that case, move Robbie there to prevent them from gaining their key type of resource.
All the remaining tips revolve around diplomacy. Moving Robbie can earn you another player's favour. The leader's strongest hex may very well have a settlement or a city of the other person. By intentionally kicking the robber out of it, you are proposing an alliance as the best tactic to play against someone who is so ahead is outnumbering them. To do so effectively, you have to ensure both you and your tag team partner are in a win-win situation. Therefore, giving them space to grow is an appropriate stepping stone.
Additionally, exposing yourself is also a considerable reason to use your Knight. As long as you keep your development cards facedown, they are deemed as Victory Points. Flipping up a Knight might helps lowers your level of threat in people's eyes. Assuming the leader currently has 08 VPs, the other player will be more likely to side with you if you have 06 VPs rather than 07 VPs.
And last but not least, trading in your turn while having one or more facedown development cards may look extremely discouraging to your counterpart. The fear of you activating a Year of Plenty, Road Building, or Monopoly post-trade would be further escalated when they are in your building vicinity. To prove that you will not double cross them, use your Knight before the trade. When they are assured you have no more tricks under your sleeves, they will feel more motivated to collaborate with you.
Bonus part: Let's raise a completely reversed question: "Providing you have fewer than 07 cards in hand, is it ever reasonable to keep your Knight face down although Robbie is blocking your best hex?". The answer is: "Yes, it is when you have other useful development cards.". In spite of having a better long-term potential, a Knight possesses a far impactless one-turn effect than all other activatable development cards. Indeed, a well calculated Monopoly, Road Building or Year of Plenty can both gain you more momentum and put your enemies in a worse disadvantage.