Oh my. I only just noticed this. Silly me.

I won't say anything about language, except to wonder whether you initially wrote this in German and then translated it into English or wrote it from scratch in English. Whatever, it's all perfectly clear to this reader.

The opening is terrific. It pulls the reader into the story straight away. I like the detail; the way you describe the action of firing an arrow and Bergens's feelings about killing. The build-up to Bergen's discovery of the body is well-managed and very tense.

I think you could drop the two paragraphs describing Bergen's and Anastasia's relationship from this chapter, and introduce them into the story later on a piece at a time, perhaps as part of a conversation. As it stands, it interrupts the action without helping the reader. Bergen isn't going to be taking all these risks if he doesn't care about Anastasia, is he? You introduce the other aspects of Bergen's character very well, though. I guess he's a professional assassin or a mercenary of some kind.

I'm sure that it's going to become clear in time how this fits in with the world of HDM. Far be it from me to criticise anybody for not writing a Lyra'n'Will story!

Just because theres no will or Lyra doesn't mean it not His Dark Materials! I think its good keep up the good work!

Great stuff here, very tense, very powerful. The desciption of Bergen and Anastasia's relationship was good, though it might've been better to imply it, or show it in a flashback after the action. I like both the characters very much, Bergen killing was well done, as was the bracelet on Anastasia's body, great personal detail.
Some language points. 'absolutely notice' should be 'surely notice', and 'fifteen minutes from now on' should be 'fifteen minutes from now'.
'Bergen was happy to have very precise information because without them he would not even have known of the tragedy to take place tonight'
Did he find the execution time out from someone? If so, the sentence should be split, if not, 'them' should be 'it'. This isn't the strongest sentence in the piece anyway. I think the second-from-final line could be put in a much more original way as well.
But, as I said, this is very good. I hope you're carrying it on, it needs a link to the rest of HDM, beyond the consequences of love, and maybe some backstory. Good luck.

Reading this chapter, I had none of the responses you obviously expected to invoke. I think the "emtional" quality of the piece was well within the "high drama" nature of the scene and characters. As far as "that ain't no HDM," my only question, of course, regarded daemons. It is conspicious that you don't mention daemons. I thought this warranted explanation (ie what world as these people from?). Perhaps you had something else in mind? A few notes on usage. In paragraph four, I'm guessing that you you meant to use "retched" instead of "belched." Also, the use of "Lady" in capitals was confusing. Because lady was capitalized I expected the girl to be royal and Bergen some kind of attendee (royal guard or something). Yet your the background for the characters (which I found to be managed nicely btw) doesn't specifiy either way. This may be the case of lacking information you planned on providing all along or a simple matter of clarity. In all, though, I enjoyed the piece. I'm curious to see if you will employ a kind of kaleidoscopic narrative effect, jumping from these kind of violent, brief character sketches, for the rest of this piece.