This is a great premise for some brilliant character dynamics and interaction and skipping ahead in time might see you lose most of it.
I would either go with
- Greater common evil - Needs must, eh?
- Forced betrayal, i.e. the monk was forced to act the way she did because she was under greater duress than what the others were aware of.
ANSWER: I would probably go uniting the team by first having them meet at the said monastery, with the betrayed party trying to get back at the monk but ending up helping her fight off her ex-monk buddies to save her aunt/daughter/brother/other organic plot device the other monks are holding captive/planning to sacrifice etc. And onwards to another tale of high adventure. Maybe this kidnapping or sacrifice was just a small part of something bigger?
Acting under duress allows for the monk to plausibly retain her criminal nature without too much of a schism with what has happened before.
Disclaimer: a large amount of the information in this answer is second-hand or generalizing from groups that wound up having a similar structure as you propose although not entirely by design. Pinches of salt all around.
It's not going to be easy
So, you have one player character who is far weaker than the other characters in combat, but wields a compensating amount of money, influence and soldiers to compensate. I foresee issues. Let's begin with the issues faced by the player of the king.
Combat is a major part of most DnD campaigns, and also where the level difference between characters is most keenly felt. Being five levels behind is a serious drawback, even in the bounded accuracy world of DnD 5e - it's a whole tier difference. While many players can deal with their characters being less useful for a few rounds, a single encounter or a single session, being constantly worse than the others can and probably will make combat seem like a chore for the player of the king. There's also encounter balance to consider - if the combats are level-appropriate for the rest of the party, the king character can quite easily get snuffed by a few area-of-effect attacks not even aimed directly at him.
So, having little power in combat is a drawback, but it can be made up with non-combat stuff like having overflowing coffers, enough soldiers to get rid of mundane threats with ease and enough influence to open the doors to anywhere, right? The difficulty here is that this can potentially detract from the experience of the other party members.
Picture the situation: the party is about to enter a fortified town that's guarded by mercenaries who refuse to let them in. Without the king, the party would have several natural choices: try to sneak around, fight the mercenaries, try to buy them off, ambush a small group of them and steal their clothes for disguises... but with the king, all the sensible solutions revolve around him: using his personal guard to round up the mercenaries, drawing from his limitless coffers to bribe them or simply appealing to his royal mandate.
The core of the issue with such a character is that it's dividing the fun bits of the game between two sub-parties - a problem commonly faced by other "skill monkey" or "social rogue" types in DnD. You have combats that are punishingly hard for the king, and to compensate, non-combat that's dominated by the king, and therefore at every moment of the game there is someone who is not getting to really enjoy the strengths of their character. You may well see people being disappointed, for instance, when the king successfully avoids combat, or conversely see the king's player get disappointed when combat is the only option.
What can you do to make it better?
Avoid building long sections of the game that emphasize some characters over others. A single short scene where the king can pull strings to ensure something nice for the party is nice, but a long scene of court negotiations while the adventurers stand leaning against the wall drumming their fingers is not very nice. Try to focus on scenes where both the party's adventurous skills and the king's wealth and influence come in handy - don't let the king's status solve all problems.
Since combat is a large part of many games, and can last for hours depending on the size of the encounters, it's rather hard to work the king in with their weakened combat abilities. Here, I would recommend a trick I've seen used a few times to give players whose usual characters were absent a bit of combat agency: instead or in addition to the king going to combat, let the king's player send two or three soldiers (personal bodyguards, champions, whatever) into combat and control them. These soldiers should be relatively simple to keep their turns fast, and to not overshadow the regular PCs. The king's player can control the champions so they have more role in combat while keeping the king relatively vulnerable as was your original intent.
Finally, you can simply make the king as powerful in combat as everyone else - it wasn't uncommon for monarchs to be capable warriors as well, doubly so in the world of fantasy. In that case, you would need to bring in the asymmetry from somewhere else, eg. by having enemies recognize and prefer to target the king in combat.
Best Answer
Zone of Truth is not what you think it is
Zone of Truth only states:
This gives whomever is under the effects quite a bit of leeway in answering.
You don't have to divulge the truth, you just can't lie.
But you can twist your words any way you'd like to not be a lie...but to not tell them the truth they are looking.
It's possible a "no" response still isn't lying.
It very much depends on what the 'untruth' is and what it means to you as a character. That is going to entirely be up to you and your DM and it can be made as such that answer "no, i'm not a traitor" is entirely reasonable. Maybe you're not a traitor to your nation, or your family, or to your friends because by being a traitor you're actually helping them. All of this is up for discussion when figuring out what 'being a traitor' actually means.
It's also important to note that whomever is asking is not above suspicion. Throwing that back is always a technique, and a very reasonable one. An innocent person is just as likely to use this tactic.
In order to do this effectively, you will have to work very closely with the DM in terms of your backstory and in terms of what information is given to the other party members that they can act on/ask about.
If they already know the right questions, then it's Game Over, Man.
Yes, they could corner you, but if they've cornered you then they already know how and why you're a traitor. If they're already that knowledgeable about the traitor in their midst, then there is little you can do.
2nd level characters don't have access to 2nd level spell slots.
The spell is also a level 2 spell and would not be accessible by a player character until level 3. No level 2 characters can do this without access to a spell scroll (and they'd risk failure with a DC 12 spellcasting ability check.)
The DM can help
If this is the way the DM wants to set up their story, they can help by providing the uncommon magic item, Ring of Mind Shielding. This item does the following (emphasis mine):
The ring works to prevent magic, like Zone of Truth to do it's job (determine if you are lying) and thus can completely prevent identification of the lie and it can be invisible. Unless they've got See Invisibility active or some way to see it (and to know to look for it), then it's an excellent way to bypass this concern. (Thanks Rubiksmoose!)
Sadly, the language isn't watertight and may still be up to the DM if it will work or not in that way. But if the DM decides it does, and that they give it to the player expressly for this purpose, then it should be fine. If a DM does not think it will, then this is not a viable option.
Player-Player antagonism in a campaign
While not directly related to this, it is most important that your table is open to this type of campaign. If players aren't expecting to be antagonist to each other or actively aren't interested in a table environment of distrust amongst each other, then this may not be a great course of action. Making sure that the table is open to and wanting an intrigue-heavy campaign that includes players possibly playing against other players is something that should be decided at the onset of the campaign prior to start.
You also need to have some sort of (very very flexible) plan for what happens when the traitor (intentionally or otherwise) reveals themselves and now finds themselves in direct and open conflict with the party. Are they ok with their PC dying? Becoming an NPC? etc.