'post-predicative' is a modern English compound formed from the Latin prefix 'post' (from Latin 'post', meaning 'after') + 'predicative' (from Latin 'praedicativus' via Late Latin/Old French, related to 'praedicare'/'praedicatum').

'predicative' comes from Latin 'praedicativus' (via Late Latin and Old French 'predicatif'), which entered Middle English as 'predicative'; the prefix 'post-' (Latin 'post') was attached in modern English usage to form 'post-predicative' to denote position 'after the predicate or modified element'.

Initially, roots meant 'after' (post-) and 'to proclaim/say' (praedicare → predicate); combined in modern linguistic terminology to mean 'positioned after what is being modified' rather than any sense of 'proclaiming'.