There is somewhat a bit of relation to maybe the very first game (I still haven't completed that one), I mean in terms of actual origin of Agent 47. This stuff is explained a bit in the tutorial stage of season 1 (in Hitman™ (2016) or in legacy pack for Hitman™ 2, I am not sure if this tutorial is available without legacy pack, as the game started directly from season 2 mission for me, not from tutorial). If you are interested - read about it on the net, there is no point in playing unless you want to foce yourself to play a very old 3d game - those aged very poorly.
As for other parts of the story, as mentioned above - this is direct sequel to Hitman™, a game from 2016. Actually, you should call them season 1 and season 2, as that is how they were originally planned. So yes, for the story - you should have played previous game, but Hitman is about replaying a game over and over, to find different ways to approach same target. This means, that story is not something that is the most important in this game, but I must say, that while first season was not about the story at all, now you really complete story missions, I won't say more not to spoil anything 🙂