What is the make and model number of the kettle?
Most likely either the heater element has burned out or perhaps the thermostat cut-off switch is faulty.
You would have to dis-assemble it further i.e. remove or loosen the circuit board so that you can access the wiring to the element so that it can be checked with a DMM (digital multimeter) and also check the cut-off switch etc. as nothing looks untoward in the image that you posted.
The hard part with most electric kettles is sourcing replacement parts, as they are considered to be “disposable” by the manufacturer and there usually are none available, but you can only try.
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