This archetype is kind of the counterpart to the Kensei. While the Kensei focuses on offense through weapons, the Defender focuses on defense through shields.
I'll try to explain the reasoning behind the features and where they come from, but most of them were heavily inspired by the Kensei Monk.
In terms of visualization, I imagine a Defender Monk fighting like Captain America. Notice how in this clip he uses the shield to attack and block, but also uses a bunch of unarmed strikes and dodges. I think this fits perfectly with the Monk class.
A different approach would be to reflavour the shield as a greatshield, so you would fight like Mash.
I tried my best to keep things balanced, but since I don't have that much experience with D&D I probably wasn't able to. Please let me know what should be changed to balance it.
Way of the Defender
Path of the Defender
When you choose this tradition at 3rd level, your special martial arts training leads you to master the use of shields. This path also includes instruction in the deft strokes of calligraphy or painting. You gain the following benefits.
Shield Mastery. You gain proficiency with shields if you don't already have it. Wielding a shield no longer prohibits the use of your Unarmored Defense, Martial Arts and Unarmored Movement features. You no longer require 1 action to don or doff a shield. A shield is a monk weapon for you and its damage type is bludgeoning.
Agile Defense. When a target other than you that is within 5 feet of you is attacked, you can use your reaction to impose disadvantage on the attack roll. You must be wielding a shield.
Way of the Brush. You gain proficiency with your choice of calligrapher's supplies or painter's supplies.
This is directly taken from the Kensei.
Instead of Kensei Weapons you get Shield Mastery and the +2 AC bonus from Agile Parry is gained through the wielding of a shield. Notice how since the shield is now a monk weapon, you can attack with it, and its damage die equals your Martial Arts die.
Agile Defense is taken from the Fighter's Protection fighting style - notice how unlike Protection, this feature doesn't require you to see the attacker. Since this archetype is focused on defense, I thought it fit better like this, in order to represent how aware of the battlefield and his allies the Monk is. Take an archer firing arrows while hiding in a brush as an example. This way, you can protect your allies even though you don't see the archer - you still see the arrows flying from above, so it makes sense that you would be able to react, I think.
One with the Shield
At 6th level, you extend your ki into your shield, granting you the following benefits.
Magic Shield. Your attacks with your shield count as magical for the purpose of overcoming resistance and immunity to nonmagical attacks and damage.
Deft Defense. When the target of your Agile Defense is hit, you can spend 1 ki point to increase that target's AC by the bonus AC of your shield. This bonus lasts until the end of the current turn, including against the triggering attack.
Again, heavily taken from the Kensei. Magic Shield is exactly the same as Magic Kensei Weapons.
Deft Strike is replaced with Deft Defense. Instead of spending 1 ki point to deal extra damage, you can spend 1 ki point to better protect your allies. This functions similarly to the Shield spell, but instead of lasting until your next turn, lasts until the end of the current turn. Basically, it allows you to protect an ally from being hit by multiple attacks from the same enemy. As for RPing, think of it as you jumping into your ally's side to protect them from attacks. Once the current turn ends (i.e. the enemy stopped attacking your ally), you return to your own position.
Strengthen the Shield
At 11th level, you gain the ability to augment your shield further with your ki. As a bonus action, you can expend up to 2 ki points to grant a shield you touch a bonus to AC while you are wielding it. The bonus equals the number of ki points you spent. For every ki point you spent, the distance at which you can use Agile Defense increases by 5 feet. This bonus lasts for 1 minute or until you use this feature again. This feature has no effect on a magic shield that already has a bonus to AC.
Very similar to Kensei's Sharpen the Blade, only instead of bonus to offense, you get bonus to defense.
The amount of ki points you can spend goes down from 3 to 2, because AC is usually a stronger stat than attack. The extra range on your Agile Defense also allows for better protection of the backline casters. Of course, the bonus to AC from this feature also affects Deft Defense.
At 17th level, your mastery of the shield grants you extraordinary defense reflexes. In combat, you get a special reaction that you can take once on every allied creature's turn, except your turn. You can use this special reaction only to use Agile Defense, and you can't use it on the same turn that you take your normal reaction.
Finally, this feature was adapted from Cavalier's Vigilant Defender. Instead of being able to do multiple opportunity attacks, you are able to do multiple Agile Defense (and consequently, Deft Defense as well).