Z590 D and second monitor output

[fonon]

Is it possible to connect a second monitor to the motherboard via internal thunderbolt connector without a dedicated expansion card? If yes - how?

[shadowsports]

Greetings,
No.  The board has a single display port.  Only one display is supported.

[fonon]

No.  The board has a single display port.  Only one display is supported.

And what's about thunderbolt connector?

[shadowsports]

No.  The board has a single display port.  Only one display is supported.

And what's about thunderbolt connector?

Greetings,
My apologies, I wasn't clear on your question.  The internal header allows you to connect a Thunderbolt card.

Gigabyte makes 5 different models. 

https://www.gigabyte.com/us/Motherboard/Thunderbolt-Card

The one for your board is the MapleRidge.  It has to be installed to the x4 slot.  You can read about it here:

https://www.gigabyte.com/us/Motherboard/GC-MAPLE-RIDGE-rev-10#kf

However, you cannot connect a display to the internal header, you must install a card.