test drove a 2011 4.4 tdv8 today.
Had a vibration around 2-3k on acceleration.
Seemed to only happen in 2nd gear.

Felt a vibration through the car and a rattle with the window open.

I've left the vehicle for now but could it be prop shaft bearing?
Or transmission.

Mileage was 100k.

Next! You could be chasing that for ever and ££
Plenty out there  Gone to a good home: 2011 4.4 TDV8 Vogue SE Buckingham Blue with Ivory and clear glass = "Rory"
2025MY Defender D350 90 in Silicon Silver on coils
1974 Series 3 Lightweight = "Millie"
Many, many other Landies over the years
My preferred specialist: www.glenrands.co.uk
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Yeah, might be something simple, but who knows.

Plenty about....move on....

 2011 Range Rover Vogue SE 4.4 TDV8

Previous cars :
2003 Range Rover Vogue TD6
1999 Discovery Td5 ES
1995 BMW M5 3.8 6 speed
1992 Range Rover 3.9 Efi Vogue
1992 BMW M5 3.8
1988 BMW 735i SE
1989 Ford Sierra XR4x4 2.9i
1981 Ford Fiesta Supersport