Final answer:
The correct usage of the phrase in question is 'onetime', referring to someone who was formerly in a position. It should be written as one word to convey the meaning of 'former' or 'past' in the given context.
Step-by-step explanation:
The question seems to be concerning the correct grammatical use of a hyphen in the phrase ‘one-time heir apparent’ related to the context provided, which is a matter of English grammar and usage. In the given sentence, the correct usage is ‘onetime’ as it is an adjective describing the heir apparent who was once considered for a position in the past but is no longer in that position. Therefore, ‘onetime’ should be written as one word without a hyphen in this context to convey the meaning of ‘former’ or ‘in the past.’
The Zimbardo reference provided for context alludes to the infamous Stanford prison experiment, which offers insight into human psychology, particularly the influence of power dynamics and authority on behavior. However, this information comes from a field of study separate from the primary grammatical focus of the question. Hence, it might not be directly relevant to the grammar query presented but instead serves as an understanding of where this type of situation, using a myriad of descriptive terms to define roles and actions, could be applied in academic literature.