My knowledge of the correct terminology is sadly lacking so other more
informed people may disagree with my below answer...
To answer your question, I would say no, "tenureship" is not a word.
The word "tenure" is a noun and the meaning of the word incorporates the
concept "‘to hold’" while other nouns such as "apprenticeship"
effectively use "ship" as a suffix to create a similar meaning when
attached to the base noun of "'apprentice'
(http://www.askoxford.com/concise_oed/apprentice?view=uk)/'owner'
(http://www.askoxford.com/concise_oed/owner?view=uk)".
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