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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.

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

And Finally, 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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Here Following is a complete example that can be used to update a checklist with a new set of items:

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