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First, you will need to create an empty collection (ArrayList<ChecklistItem) that will contain the new items.

def ArrayList<ChecklistItem> newChecklistValue = new ArrayList<ChecklistItem>();

You then create an item , and add it to the collection and finally update the custom field passing it the newly created collection.

// Create a new Checklist
def ArrayList<ChecklistItem> newChecklistValue = new ArrayList<ChecklistItem>();
def item = checklistCustomFieldType.getSingularObjectFromString('{"name": "item name"}');
newChecklistValue.add(item);

And you finally update the custom field passing it the newly created collection.

// Update the issue with the new checklist
checklistCustomFieldType.updateValue(checklistCustomField, event.issue, newChecklistValue);

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