Neil Slater's answer, which I would characterize as a "do what works best for your table" approach, is certainly a good one. Nevertheless, I shall offer a different, more proscriptive view.
Not only are you not required to reveal what action an NPC has readied, in most cases you should not do so.
The PHB's familiar guidance at p. 6, "How to Play," is instructive:
- The DM describes the environment.
- The players describe what they want to do.
- The DM narrates the results of the adventurers' actions.
The DM's job is thus twofold: providing a visualizable world for the players to act upon, and then revealing what results from their agency, thereby furthering the story.
This is a very "show, don't tell" system. When, e.g., the players encounter a trapped door, ordinarily the DM does not simply inform the players that the door is trapped. Doing so would rob the players of their job, which is to act on the door. The better practice is to describe the door. That way, the players get to engage the door and its trap on their terms -- e.g., choosing whether they will investigate, and if so, how. Maybe they use their skills, or spells, or other tools. Or maybe they chance it and simply open the door. Whatever they choose to do, the point is that it should be their choice.
An NPC is not a trap, of course, but I would submit that an NPC is nevertheless part of the "environment" -- the visualizable world that it is your job, as DM, to provide.
Consequently, the same "show, don't tell" reasoning that applies to the rest of the environment applies equally to NPCs. When an NPC readies an action, you should not simply inform the players. Instead, describe the NPC's posture, gestures, or facial expressions. Have the NPC brandish a weapon and snarl or shout "Come at me, coward!" In short, give players their agency: invite them to draw conclusions with incomplete information and to choose how they will engage the NPC on their terms. Maybe they chance it and rush the NPC. Maybe they themselves choose to hang back, refusing to be baited by the NPC you've described as nimble and shifty. Maybe they spend an action using Wisdom (Insight) to discern the foe's intentions. Such moments are the stuff of action movies -- combatants circling each other, eyes narrowed, searching for an opening.
What about Passive Perception and Passive Insight?
The "show, don't tell" approach works even for PCs of exceptional perspicacity.
Consider again the trapped door. Even if the party's rogue has a Passive Perception of 23, that does not make her omniscient. It simply entitles her to more and better detail about the door and/or the trap. Maybe she notices the telltale spatter of dried poison droplets that have been dripping down onto the floor below the doorknob for decades. Maybe she immediately spots the needle protruding just above the handle. She has plenty of excellent information to work with -- but it is still her job to draw the conclusion, "This door is trapped."
Similarly, what if an NPC assassin readies an attack against the PC cleric with a Passive Insight of 23? Just give the player more and better information. Don't be subtle. Telegraph the assassin's intentions with every sign you can think of. The assassin's fingers twitch on the knife held lightly in his hand. His wide, unblinking eyes follow the cleric's weapon. You can even use the word "ready" -- just use it as a description, not as a statement of game mechanics. Don't say, "The assassin readies an action." Say something like, "The assassin stands poised on the balls of his feet, ready to spring at the first sign of an opening."
A further benefit of using passive abilities this way is that it makes players' character-building choices more meaningful. If the PCs need to rely on their Wisdom (Insight) for information about what NPCs intend in combat, they have added reason to care about their skills. While the party's fighter squares off uncertainly with the shifty NPC assassin, using his action to try to ascertain what the assassin has planned, the player of the cleric with the Passive Insight of 23 gets to feel special when he doesn't need to spend an action that way. He's so insightful that he instinctively knows what's coming, and he can act on that knowledge.