2003 A8 D3 timing belt replacement
 

I've my timing belt done by the audi specialist. But is there another belt that need doing inside the black butterfly shape plastic towards the top of the engine. Please advice

Nope. The only belt inside the cover is the timing belt. The other belt that is visible drives the power steering, radiator fan, and air conditioning compressor. I would suspect they would have put a new one on when you had the timing belt changed.

HTH,
Dave

What you are describing is the sepentine belt. The Serpentine belt is not necessarily replaced at the same time as the TB and has a different service interval.

If unsure of age and mileage, the serpentine belt is simple and relatively cheap to replace. I think the interval for the SB is every 60k miles. The TB is 105k miles.