Here's some food for thought on the first 4 bars. But don't just look at the first 4 bars, try and look at the rest of the sheet and apply these things as a place to start.
Transcription: Don't rely on what anyone else has written before you, listen to the song and learn to develop and trust your ear. Part of arranging isn't just making sheets, it's also developing your ear skills. Anyway, there were a couple of wrong notes and some missing harmonies which I corrected.
Dynamics: It starts off quite bold and punchy and then it grows into the 4th bar. So write it!
Articulations: Articulation is everything is jazz. I'm not sure if you've had much experience playing jazz, in particular playing big band charts, but having the knowledge of what various articulations mean really helps you to be able to communicate your intentions more clearly. Take a look at what I've done and if you have any questions, feel free to ask.
Note lengths: This ties in with articulations somewhat, but you need to pay more attention to the actual length of the notes being played. If it's a short quaver, don't tie it over to the next beat etc etc. Again, having knowledge of the style and how these things are written will help you here.
And just a little thought for bars 5-12: Be careful which parts you choose to combine and how so that you don't end up with note soup. By that I mean having a whole lot of notes that then lose their meaning. An important part of arranging for piano is listening to what the most important elements are (ie what makes this tune sound like this tune) and then using or combing those in such a way that evokes the same "feel" as the original tune. In other words not necessarily using as many notes as possible from the original tune.