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I am retro fitting a new engine to my tired John Deere GT235 (over 2000 hours).
Purchased a new 24HP Briggs & Stratton Professional Series motor.
The starter has only one terminal. By supplying battery(+) to terminal the starter runs.
Engine is a Model 44S877-0002G1, Code 150922YG. Suspect I also need a starter relay, yes?
Suggestions on what to buy?

Yes, you need a remote-mounted relay (solenoid). Two types are available, 3 terminal and 4 terminal, depending on your setup. Most likely a 3 terminal will work just fine. Here is a link to a universal 3 terminal solenoid: 12 Volt Starter Solenoid Universal 3 Pole style can be mounted from side or base.

The two large terminals are for feeding the starter and the solenoid is connected between the battery and starter via two battery cables from the positive battery terminal. The small terminal is the "S" terminal from the ignition switch. Make sure the area that you mount the solenoid is clean, bare metal with a good ground as the solenoid grounds through the mounting bolts on this particular solenoid.

Just buy a starter solenoid from most any auto parts store will do.

Thanks for the confirmation. Will get it tomorrow. Stay with me, as I'm sure I'll have more things to unravel and sort out.