When I use kick down to accelerate on overtaking it gets to a point and then the engine stutters like it has an limiter on it.

If I increase the speed on the pedal normally I do not get any hesitation.

Does the engine have a limiter? or has anyone else had this happen to them?

Its a diesel engine

At what point do you experience the stutter?

Which diesel do you have?

Mind you the limiter is around 4500rpm on both td6 and tdv8 engines and it wont rev past that point. There is nothing that can't be fixed with a hammer😜😜
FFRR 4.4 SDV8 Autobiography Santorini Black.
KIA E-Niro 4+
2021 Discovery 5 D300 MHEV commercial

its at high rpm but seems to me that the box should change gear but just seems to hold itself and not change up

It a newish box that was fitted about 20k ago at a LR main dealer

It should kick up to the next gear before you get to the red line even withe your foot planted.

Have you had it long? The gear box may take a little while to adapt to your driving style? There is nothing that can't be fixed with a hammer😜😜
FFRR 4.4 SDV8 Autobiography Santorini Black.
KIA E-Niro 4+
2021 Discovery 5 D300 MHEV commercial

Only had the car for about a week or so now and was my first time to try out the kick down its not my normal way of driving but nice to know it works just in case I should need it

So long as it shifts smoothly under normal driving conditions there should be little to worry about.  There is nothing that can't be fixed with a hammer😜😜
FFRR 4.4 SDV8 Autobiography Santorini Black.
KIA E-Niro 4+
2021 Discovery 5 D300 MHEV commercial

ok no problem at all under normal driving

Here's a weird thing... You have perfectly described an issue I have.
....but mine is a petrol SC, which has a different gearbox

If I leave my foot planted it will change up , but takes a few seconds longer than it should.

Never had it looked into as car is fine rest of the time and I don't really want to know  Alcohol and eBay is never a good mix

2006 4.2 Supercharged, Java Black