I have the latest drivers. I tested audio with your realtek drivers. Using HDMI cable I get sound on earphones plugged to display. Using TB cable on this TB enabled device -- DOES NOT send audio through. Why?
Which model NUC?
Which brand/model display?
What type of cable connection between NUC and display?
My NUC8i7BEH sends audio properly to my Acer T232HL display integrated speakers with all of the following connections:
In all cases, the "Intel Display Audio" driver that gets installed by the Intel HD Graphics driver is the driver supporting HDMI audio going to the display's audio endpoint.
Just tried headphones plugged into my HP Envy 32 Media Display driven by a NUC6i7KYK via several different methods, including DP cable direct, HDMI cable direct, TB3 cable to an HP Elite/ZBook TB3 Dock, then to the display via DP cable, USB-C to DP adapter, or USB-C to HDMI adapter. The headphones sound is functional & normal in all cases. This confirms that the NUC can fundamentally send both A & V out the USB-C/TB3 port and over a TB3 cable to the display.
As indicated before, digital audio over a cable link for displays such as DP, HDMI, USB-C or TB3 is NOT supported by the Realtek audio driver but rather the Intel (R) Display Audio driver, which is typically bundled with Intel HD graphics driver releases. The Realtek audio driver supports only the NUC onboard HD Audio devices, not any display-integrated audio devices. I'm using a pretty recent Intel Display Audio driver 10.26.0.6, dated 1/8/2019, with my NUC6i7KYK (Skull Canyon). I repeated the testing with my NUC87iBEH (Bean Canyon) and NUC7i5BNH (Baby Canyon) with identical working results.
Your display (which you did not provide brand/model) can support AV over HDMI, but it may have an issue supporting audio over TB3.
In Windows Device Manager, under the "Audio inputs and outputs" section, look for an audio endpoint device corresponding to your display. My system shows a "HP ENVY 32 (Intel(R) Display Audio) device. If you don't see any audio device in this section with "(Intel(R) Display Audio)" in its description, it means the audio playback endpoint of your display is not seen by Windows, so you will get absolutely no audio from your display.
Your display is more likely to be the culprit than your NUC (NUC7ixBNx Baby Canyon?). Another possibility would be a bug in the Intel Display Audio driver.