https://salesforce.stackexchange.com/questions/255128/how-to-handle-lightning-web-component-event-from-lightning-aura-component

componentA.js

import { LightningElement } from 'lwc';

export default class ComponentA extends LightningElement {
    fireEvent() {
        // Fire DOM custom event
        const customEvt = new CustomEvent('custom');
        this.dispatchEvent(customEvt);
    }
}

componentB.cmp

<aura:component 
    access="global" 
    implements="flexipage:availableForAllPageTypes, forceCommunity:availableForAllPageTypes">

    <aura:handler event="c:appEvent" action="{!c.handleApplicationEvent}"/>
</aura:component>	

componentBController.js

({
    handleApplicationEvent : function(component, event) {
      // Handle the event in your Aura component (component B)
      
    }
})

newAuraComponent.cmp

<aura:component 
    access="global" 
    implements="flexipage:availableForAllPageTypes, forceCommunity:availableForAllPageTypes">
    
    <aura:registerEvent name="eventofComponentB" type="c:appEventt"/>
    <c:component-a oncustom="{!c.handleCustom}"/>
</aura:component>	

newAuraComponentController.js

({
    handleCustom : function(component, event) {
        var appEvent = cmp.getEvent("eventofComponentB");
        // data from lwc event to pass to the aura event
        appEvent.setParams({"lwcEvent" : event });
        appEvent.fire();
    }
})