(I am NOT an expert in video editing but for what it's worth)
It would be better if you don't see the assassin's face at the start or until the end or in fact, at all.
The assassin actually doesn't need any dialogue. The audience knows the target and what he needs to do from the screen he was looking at.
You don't actually need to see him put away the gun, the glimpse of the gun shot from the victim into his bag is enough a clue.
The music doesn't quite suit. You are trying to portrait urgency and secrecy, however, the start should be something mundane, or even happy, as is the state of mind of the victim, since he doesn't know he is about to be killed. Later on, during the chase, you can then speed things up. (do you remember the corridor scene in which Darryl Hannah walks down to inject Uma Thurman with poison in Kill Bill?) Again, at no time you actually need to see the assassin's face. Perhaps a shot of his eye right at the end.
Less is more.
What you get hopefully is the audience forming a bond between the victim but keep the assassin at a distance thus create a mystery and hopefully a sense of fear with that too. By showing his face, the gun and giving him a voice. You have personalised him and bring him down to a common thug rather than an assassin.