Existing Logo Refresh Needed

You can download my current logo here: https://limewire.com/d/iukLY#fl0wJclMso. I want to keep the identity people already recognise but give it a sharper, more contemporary feel that works just as well on a phone screen as it does on printed material. Feel free to refine the colours, typography, or proportions—whatever you think will modernise the mark while preserving its essence.

When the design is approved, I’ll need:
• An editable vector file (AI or SVG)
• High-resolution PNG with a transparent background
• JPEG for quick previews
• A brief note on the final colour codes and fonts used

Show me how you’d evolve the logo and keep its spirit intact.