Well then, if it's AC, you have two choices.
1. - Have a ridiculously long extension cable trailing you
2. - Have a ton of batteries hooked up to an inverter, not very weight efficient.
I have done "self drag racing" with my Briggs flathead kart, but that is in no way similar to an electric motor.
Can we at least see some pics of the motor? I feel like it's a massive industrial motor, designed to spin at low RPM, or possibly on a low duty cycle.
As itsid said above, a clutch on an electric motor is quite pointless, not to mention extremely inefficient.
Let me put it this way: You pull up to the christmas trees with a directly driven electric kart, the lights tick down, and you launch. There is minimal moving parts, and the motor does not need to spool up. = Faster launch times.
But with a clutch, the motor has to spool up to reach engaging, so that means lost time, not to mention the small amount of slip in the clutch, which further kills the ET.
Electric motors produce maximum torque INSTANTLY, as soon as you touch the "gas pedal". That is equivalent to a hard clutch dump.
If I had money, I'd be willing to bet that a properly geared direct drive electric kart would outperform it's own clutched setup at the dragstrip.
However, I can't stop you from going down the rabbit hole, so here's a 1 1/8" bore Comet 94C Duster torque converter driver pulley.
https://6x6parts.com/4_cycle_engine_clutch_pulley__1_1_8-_bore.html
$265!!!!!
And you still need a driven pulley and belt! Not to mention a way to mount it!