'partially-approved' is a compound of 'partially' and 'approved'. 'Partially' ultimately originates from Latin 'partialis' (from 'pars' meaning 'part'), formed in English from 'partial' + the adverbial suffix '-ly'. 'Approved' comes from Latin 'approbare' ('ad-' + 'probare'), via Old French and Middle English 'approven'/'approve'.

'partialis' (Latin) → 'partiel' (Old French) → 'partial' (Middle English) → 'partially' (Modern English adverb). 'Approbare' (Latin) → Old French 'aprover'/'aprover' → Middle English 'approven' → Modern English 'approve' (past participle 'approved'). These elements were combined in Modern English to form the descriptive phrase 'partially approved' (often hyphenated when used attributively).

Initially the components meant 'in part' ('partially') and 'to give assent or confirm' ('approve'); combined in modern usage they mean 'approved in part' or 'approved to a limited/conditional extent'.