Is there a way to create a new polyline covering the green layer from one point of intersection with the blue layer to another (the new polyline should be on the same layer as the green entity)?
Open border pline tracing
Kind of hard to tell what color is what with your gray background screen capture.
My best guess is that you want what I've drawn in RED as the new boundary?
Perhaps share your dwg?
If the other entity you're referring to is the Blue Boundary then yes, just selecting the Green or newly created Red Boundary as the Cutting Edge and that will give you this result:
Just be aware of the effect of having both selected as cutting boundaries, if you want to do it in one Trim command. If a Polyline is among the cutting boundaries, when you pick on a segment of that same Polyline, only that segment is removed [or part of it, if it is crossed by another cutting boundary object]. So you can either:
A) select both as cutting boundaries in one Trim command, and pick multiple times on each within the area you want to remove [once in every applicable segment or portion], or;
B) use two Trim commands, with one selected as cutting boundary and the other picked to be Trimmed to that, anywhere within the part you want removed -- it will take out multiple segments and portions of segments with one pick.
Kent Cooper, AIA 
