Corn has ears. This is an ear of corn.
When the outer leaves of the corn become yellow, it is autumn. Coroners are judges who investigate causes of death. In the British legal system, every death is investigated. If there is doubt over the cause of death, of if the death might have been preventable (and particularly if it may have been a crime) then a special judge will hold an investigation, like a trial, to discover why a person died, and if there is anything that we could learn from it.
"Yellow scorch on the leaves of ears of corn" is being used as a poetic way of saying "Autumn". And the coroners get ready for duty because (it is implied) that there are more unexplained deaths in autumn and winter, apparently because the country is (metaphorically) burnt out, in the way that when a candle burns up all the wax, the wick burns away and the candle goes out.