Do not improvise an alternative supply to work around a fault. A disposer sits in a wet working area, and the manufacturer's electrical requirements and the condition of its normal supply need proper assessment.
What the observation tells you
An extension lead that makes the motor run does not explain why the original arrangement failed. It can also leave connections in unsuitable positions under the sink. Avoid moving plugs through wet areas or opening electrical accessories to investigate.
A useful next step
Keep the appliance out of use and book the appropriate electrical or appliance assessment. Tell the engineer whether a protective device operated and which other equipment was affected.
Manuals and supporting guidance
Model-specific instructions take priority. These references support the practical principles discussed here; they do not diagnose your appliance.