A developer has just released both a 3D printed design and PCB layout for an open-source Sega Master System to Game Gear cartridge adapter, called the MS2GG: https://github.com/ms2gg/doc/wiki
This would be a replacement for original cartridge converters, such as the Master Gear Converter. Since the Game Gear is essentially a portable Master System, you get pretty much full functionality with the Start button mapped to Pause.
As a note, you’ll need to keep realistic expectations on how this will look, as you’re essentially squishing the SMS’ 256×192 resolution into the Game Gear’s 160×144. While this was a pretty awesome thing to own when the Game Gear was new, using it today means a significant downgrade in video quality using original screens (left pic), however it’ll look great if you’ve installed a modern LCD screen (click for full-sized):