The add-on Flames of Vengeance picks up where D2:ED ends, in a seamless transition. It is available as a digital download on the PC, or as part of DKS (remastered D2:ED + FoV) on the PC and Xbox (there should be an announcement Monday on when the North American release of the Xbox version and physical US PC version of DKS will be).
Wait ... ... Do you, Aboz, finished Divine Divinity(DD)?? Or Divinity II ??? Because you're here in the forum selection of DD = Divinity I !
On 7th of february 2015 : I start a new adventure in the Divinity world of Original Sin, it's a Fantastic Freaking Fabulous Funny ... it's my All Time Favorite One !
There is not always an option to do this in every game, however I would suggest going to my source site to investigate the matter further. Usually such games will say "New Game +" at the main menu or start a new game automatically when you load the data containing the completed save file.