Back in Season 5 of Game of Thrones, Cersei made the tragic mistake of making the High Sparrow the High Septon and Westeros has never been the same. Since taking power, the High Sparrow has locked up Loras, Margarey Tyrell, and Cersei, made Cersei do a walk of shame, and has influenced Tommen to get rid of the trial by combat. The High Sparrow has officially taken over Westeros. Thankfully the High Sparrow's reign may finally be coming to end but what would the High Sparrow's death mean for the rest of Westeros?
As the Season 6 finale draws, near many fans believe this may finally be the end for the High Sparrow. Whether Cersei really does break out the wildfire and burns King's Landing to the ground, or Margaery is somehow able to convince Tommen that the High Sparrow needs to go, the High Sparrow will hopefully be going down. With his death, the Faith Militant will most likely be disbanded as well.
After the mess the High Sparrow created, there probably won't be another High Septon. Giving the High Sparrow that much power was Cersei's biggest mistake, and if Tommen (or whoever is running King's Landing) is smart, they'd make sure to never give someone that much power ever again. If they do pick a newHigh Septon, it's be someone that can be controlled and used however the king wants them to be.
If there was a High Septon again there would definitely be a separation of church and state. The religious leader would not be able to hold trials, jail people, or do anything really, other than hold services. The ruling houses have since learned that it's in their best interest to keep the power in their hands and won't ever let it slip again. Similarly, anyone that supported the High Sparrow, such as Cersei's cousin, Lansel, will probably be put to death or locked up, so there's no uprising.
The death of the High Sparrow would also bring the end of religion and state, and the return of the houses back to their proper rule. Clearly there is a lot to look forward to.