Peerless Transmissions (formerly part of the Tecumseh organisation but now owned by Husqvarna) has made many models of transmission over the years. Yours is called the 601 Series Slow Speed Transaxle, and there are workshop manuals for it available from various sources. One of these is the large (1462 page) compendium of Peerless workshop manuals, which is available for download from the ride-on mower part of the Outdoorking manuals section. This is a subscription area.
To inquire about a kit I suggest you contact the Outdoorking on-line store. If you have specific questions once you have parts and information to hand, just post them in this thread.
