After browsing around a while, I noticed that many...I think almost all...large turbofans have this gap between the LP turbine and HP turbine. I took some screenshots and put a red circle around the gap.
Why do they have this gap? It's certainly not for the combustion chamber. That part comes before the LP turbine. The only thing I can think of is the LP and HP are on different spools so maybe they need some space for the bearings to brace the two shafts. But there should be bearings bracing the shaft all along its length so idk.
I'm guessing it would be more efficient to eliminate this gap and should allow a smooth transition from high pressure to low pressure. At the very least it would save some room at the end of the engine, shortening its length and maybe saving some weight.
EDIT: At first I thought it was totally empty. But it appears that space has stator vanes not shown in the pictures. I'm editing the title with the phrase "gap of turbine blades" because the original spirit of the question was about way there's a big space between the two sets of turbine blades. The space happens to have something else in it, but not turbine blades and I was wondering why those sets are separated.