If I installed a mod that changes Tremere outfits, for example, but I want to use the 3rd armour of that mod as the 4th armour for another Clan, should I just rename all the files & folders to the armour/Clan I want it to be?

Thanks in advance!

Changing the folder names won't help. If you want to swap models between clans, better edit clandoc000.txt.
You cna find the file in /unofficial_patch/vdata/system.
Open with notepad (or the texteditor of your choice, I use notepad++) and search for entries like Player_Brujah.
In each block for a clan you find these lines:
"Clan" "Brujah"
"M_Body0" "models/character/pc/male/brujah/armor0/brujah_male_armor_0.mdl"
...

This is the easiest way to swap appearance around between the clans or to make the third armor the first etc.

If you want to use the outfit you downloaded for the Tremere and for the other clan, the above is the way to do it. But if you want to keep the original model for the Tremere it becomes complicated.
In that case, leave clandoc alone. Copy all files into the appropriate model and texture folders for the other clan. And now you need the vpktools. They are part of the patch extras.
Use the model tool, open the model files you just copied and change the texture path accordingly. Otherwise the game would try to use the original Tremere texture.

I'm trying to use the third armour (the Therese one) of this mod (: https://www.moddb.com/games/vampire-the-masquerade-bloodlines/addons/female-toreador-reskin-jeanette-model-pack) as the Malkavian Heavy Leather/Body Armour.

So far, I've changed all the file names in the toreador model folder to malkavian_female_armor_3 (or something along those lines) and extracted the RED Jeanette folder as instructed.

Everything in the Unofficial Patch folder, of course.

Nothing changed so far.

EDIT:

So my best bet would be to install the mod as instructed, and then change the models in clandoc000.txt?

I've edited my clandoc000.txt (in the Unoffical Patch folder) to this.

General
{
"Clan" "Malkavian"
"M_Body0" "models/character/pc/male/malkavian/armor0/Malkavian_Male_Armor_0.mdl"
"M_Body1" "models/character/pc/male/malkavian/armor1/Malkavian_Male_Armor_1.mdl"
"M_Body2" "models/character/pc/male/malkavian/armor2/Malkavian_Male_Armor_2.mdl"
"M_Body3" "models/character/pc/male/malkavian/armor3/Malkavian_Male_Armor_3.mdl"
"M_Body4" "models/character/pc/male/malkavian/armor3/Malkavian_Male_Armor_3.mdl"
"M_Body5" "models/character/pc/male/malkavian/armor3/Malkavian_Male_Armor_3.mdl"
"F_Body0" "models/character/pc/female/malkavian/armor0/Malkavian_Female_Armor_0.mdl"
"F_Body1" "models/character/pc/female/malkavian/armor1/Malk_girl_Armor_1.mdl"
"F_Body2" "models/character/pc/female/malkavian/armor2/Malk_girl_Armor_2.mdl"
"F_Body3" "models/character/pc/female/toreador/armor3/toreador_Female_Armor_3.mdl"
"F_Body4" "models/character/pc/female/toreador/armor3/toreador_Female_Armor_3.mdl"
"F_Body5" "models/character/pc/female/toreador/armor3/toreador_Female_Armor_3.mdl"

It still uses the default Malkavian armour for Hvy Leather & Body Armour.

Tested it again and again, it still uses the basic Malkavian armour.

Mind, the mod I installed works perfectly for a Toreador character.

So if I understand you right, this is a mod for Toreador armor. You want to use one for the Malk and don't care what the Toreador looks like.
In that case, you don't change any file or folder names. You just copy the files into the unofficial_patch subfolders and edit clandoc.

That's what I wanted to do. But changing Clandoc didn't work.

It's solved. It boiled down to me not noticing that the proper name is "malk_girl_armor" instead of "malkavian_girl_armor."