Angel Heart

Plot: A young Taiwanese assassin codenamed "Glass Heart" committed suicide by
jumping off a building, and her heart was pierced by metal fence.
Miraculously, her life was saved by heart transplantation. During her
recovery she began to experience strange dreams, which lead her to
Japan looking for the donor of her heart, who happens to be Kaori
Makimura, former partner of City Hunter Ryo Saeba.

This is considered to be a sequel to the famed City Hunter series where Saeba Ryo was introduced.
The beginning was promising but then they kinda lost the plot.
At 50 episodes it is a tad too long(in my opinion) but worth a watch nonetheless.

I seem to remember watching a movie with pretty much the same plot (live action) It was chinese in origin I think... wonder if there is any connection.... it was way too long ago though... dont remember the name...

I take back my words on the series.I was still in the middle of watching it when I made this thread.
The show doesn't have a particular aim or climax but instead it chronicles the life of the assassin who is brought back into the mainstream of society by Saeba Ryo.

Spoiler:

The animation and the drama are also pretty damn good.
And the ending song is a delight to the ears.

https://www.youtube.com/watch?v=lgySXZOGDss