The 13th Doctor was meant to be the last incarnation of the Doctor but he was`nt. This Doctor met his end after blowing up Skaro with a Neutron bomb as well as destroying the Daleks (maybe).
When his previous incarnation regenerated he turned into an aggressive doctor than before because he commited geno-side destroying daleks after saying there phrase EXTERMINATE!!!!!.
He was the shortest living doctor on the regeneration cycle only lasting only a few hours alive thous not having regeneration sicknes and been immune to radiation poising because his previous self regenerated in an energy pit.
When he blew up skaro he damaged his body and the tardis but he had enough strengh to go send his last 12 incarnations messages of there future.
But when he got back to his ruined tardis he fell on the floor and started to die and having one last visit from The Observer meanwhile before he died the doctor stated he did have a fear of dying and then he died (for a few seconds).
But he woke up with a new body in a new regeneration cycle having a 14th incarnation to his timeline the observer explained he was granted a new regeneration cycle because he was the last of the time lords and the saviour of the universe the doctor yelled that IT WAS FORCED UPON but then The Observer left and The Doctor accepted that he was granted another regeneration cycle and started more adventures.