The work of ministry is accomplished by the saints - not the Apostles, prophets, evangelists, shepherds, teachers.
ESVAnd he gave the apostles, the prophets, the evangelists, the shepherds and teachers, to equip the saints for the work of ministry, for building up the body of Christ,
The Greek New Testament: SBL EditionChapter 4εἰς ἔργον διακονίας
εἰς- Purpose clause by most commentaries, some with reference to.
Either way - εἰς points the equipping of the saints is to the work of the ministry. The saints are to do the work of the ministry.
διακονίας - service, administrative function.