Discovery TD5 power inconsistency.

Im hoping someone can provide a little info on engine behavior that I can't figure out. I've just inherited a 2002 discovery td5 ES. It's great and runs beautifully. However, when cold the car is very slow to accelerate in each gear until the turbo kicks in. After a few miles, if I let out the clutch a little more slowly and increase the revs a before fully releasing the clutch it sounds like I engage a new level of power. Do excuse my terrible knowledge of cars and landrovers, I hope I am explaining this correctly. Essentially once this has happened the car accelerates from the word go in every gear. It's as though another turbo has engaged for the lower rev range.
Does anyone know whether this is normal or whether there may be an underlying issue like the clutch for example?

Any advice would be great.

Thanks.

If u dont know it's history the first simple things to do are: replace the fuel filter, check the EGR valve(if u still have one), check the ECU's red plug for oil ingress. ... then u can go further, i think u'll get some info here or insert keywords in the forum's search engine.