I have never added one, but I've certainly had to write my own version of the \common\template_windows.xml templates for tabs_charsheet and tabs_recordsheet. That's the raw code that I overwrote because I needed to be notified when tabs changed and had to add that code in myself. The only reason I needed to do the xml's was because they are what point to the script file and I needed it to point to my version of it. I tell you this because all things with tabs start with these templates and the
<script file="common/scripts/buttongroup_tabs.lua" />
When dealing with the charsheet you need to understand that you'll need to create a merge version of 5E\campaign\record_char.xml in your extension. Looking at this file you can see where the tabs are defined - there are 7 of them. Be aware other people write extensions and if you go off and break the world to fit your stuff in you'll probably break them to if they touch that. I'm purposely ignoring any extensions outside of these 7 in my current extension so it should not impact me.
Here is the relevant chunk of that xml that deals with tabs..
<sub_charsheet name="main">
<class>charsheet_main</class>
</sub_charsheet>
<sub_charsheet name="skills">
<class>charsheet_skills</class>
</sub_charsheet>
<sub_charsheet name="abilities">
<class>charsheet_abilities</class>
</sub_charsheet>
<sub_charsheet name="inventory">
<class>charsheet_inventory</class>
</sub_charsheet>
<sub_charsheet name="notes">
<class>charsheet_notes</class>
</sub_charsheet>
<sub_charsheet name="logs">
<class>charsheet_logs</class>
</sub_charsheet>
<sub_charsheet name="actions">
<class>charsheet_actions</class>
</sub_charsheet>
<tabs_charsheet name="tabs">
<tab>
<icon>tab_main</icon>
<subwindow>main</subwindow>
</tab>
<tab>
<icon>tab_skills</icon>
<subwindow>skills</subwindow>
</tab>
<tab>
<icon>tab_abilities</icon>
<subwindow>abilities</subwindow>
</tab>
<tab>
<icon>tab_inventory</icon>
<subwindow>inventory</subwindow>
</tab>
<tab>
<icon>tab_notes</icon>
<subwindow>notes</subwindow>
</tab>
<tab>
<icon>tab_log</icon>
<subwindow>logs</subwindow>
</tab>
<tab>
<icon>tab_actions</icon>
<subwindow>actions</subwindow>
</tab>
<activate>1</activate>
</tabs_charsheet>
That's it. Each of those tabs hold a subwindow which holds a class which you can look up elsewhere - but you'd obviously have your own new subwindow and class of your own.
All the tab logic is buried in the tabs_charsheet template (remember I mentioned it earlier and the code tied into it).
I suspect to add a new tab you'd do something like this (not sure - don't blame if it doesn't work I've never done it - this is theory)...
In your extensions version of record_char.xml...
<root>
<!-- Add your stuff to the character sheet -->
<windowclass name="charsheet" merge="join">
<sheetdata>
<sub_charsheet name="YOUR_STUFF">
<class>charsheet_YOUR_STUFF</class>
</sub_charsheet>
<tabs_charsheet name="tabs" merge="join">
<tab>
<icon>tab_YOUR_STUFF</icon>
<subwindow>YOUR_STUFF</subwindow>
</tab>
</tabs_charsheet>
</sheetdata>
</windowclass>
</root>
where that charsheet_YOURS_STUFF is something you make yourself based on the 7 other examples you have to work with.
Now - none of this may work.
But that is my guess based on having had to rewrite parts of the core of it.
Then in your code you can mess around with the nitty gritty if you need to with stuff like this.
local nActiveTab = window.parentcontrol.window.tabs.getIndex();
Good luck - if it doesn't work - that's all I got :)