I always love the phrase 'non political parish council', there is nothing to stop anyone being political. However that is an aside.
If there are candidates, I.e. there is an election it is perfectly reasonable to display the official statement of persons nominated, but not anything else.
If they are elected unopposed, then once the election date is past the Clerk can produce a document, if this is a standing procedure - otherwise you have to consider who instructed the Clerk to do it - the old council. I wouldn't want the Clerk to do anything until after the election date and instructed by the new council.