Crisp Print-Ready Logo Upgrade

I need my existing raster logo recreated so it can be printed sharply on large-format banners. At the moment I only have a JPEG/PNG, so the first step is to cleanly redraw the mark in full vector, preserving every detail and colour exactly as in the original. Once the artwork is rebuilt, I’ll need final files that meet standard press specs for banner production—CMYK AI or EPS as the master, plus a high-resolution PDF and a transparent PNG for other uses.

Please ensure the paths are tidy, colours are properly converted, and the design remains perfectly scalable without pixelation. If anything about the source art seems unclear, show me a quick proof before you finalise the files so we avoid surprises at print time.