HCSB: for the administration of the days of fulfillment — to bring everything together in the Messiah, both things in heaven and things on earth in Him.
ISV: to usher in the fullness of the times and to gather up all things in Christ, both things in heaven and things on earth.
NET: toward the administration of the fullness of the times, to head up all things in Christ – the things in heaven and the things on earth.
The NET Bible comments as following on the word ἀνακεφαλαιώσασθαι:
The precise meaning of the infinitive ἀνακεφαλαιώσασθαι (anakefalaiwsasqai) in v. 10 is difficult to determine since it was used relatively infrequently in Greek literature and only twice in the NT (here and Rom 13:9). While there have been several suggestions, three deserve mention: (1) “To sum up.” In Rom 13:9, using the same term, the author there says that the law may be “summarized in one command, to love your neighbor as yourself.” The idea then in Eph 1:10 would be that all things in heaven and on earth can be summed up and made sense out of in relation to Christ. (2) “To renew.” If this is the nuance of the verb then all things in heaven and earth, after their plunge into sin and ruin, are renewed by the coming of Christ and his redemption. (3) “To head up.” In this translation the idea is that Christ, in the fullness of the times, has been exalted so as to be appointed as the ruler (i.e., “head”) over all things in heaven and earth (including the church). That this is perhaps the best understanding of the verb is evidenced by the repeated theme of Christ’s exaltation and reign in Ephesians and by the connection to the κεφαλή- (kefalh-) language of 1:22 (cf. Schlier, TDNT 3:682; L&N 63.8; M. Barth, Ephesians [AB 34], 1:89-92; contra A. T. Lincoln, Ephesians [WBC], 32-33).[2]
We see a variety of translations of the word anakephalaiomai, but one thing is certain, all things will be in/under Christ, whether that means salvation of all people or something else. The easiest translation to understand the meaning of the verse/word seems to be the NET. Paul here is writing about the coming exaltation and sovereignty of the Lord Jesus Christ over everything that is created. This is further supported by other writings of Paul about the coming reign and exaltation of the Lord Jesus like Colossians 1:16, where we are told “For by him all things were created, in heaven and on earth, visible and invisible, whether thrones or dominions or rulers or authorities—all things were created through him and for him.” All things were created for the glory of the Lord Jesus. All authority is the Lord Jesus’ (Mt 28:18); the Father has put everything under his feet (Eph 1:22; Heb 2:8; 1Cor 15:24-28); the Lord Jesus is the head of all rule and authority (Col 2:10); everyone will bow down to Him, whether as servants or as defeated enemies (Phil 2:10). See also the use of Colossians 1:20 by Universalists or Universal Atonement advocates here. That is a text which to the sovereignty of Christ much like this passage here.
There seems to be no reason to think that this verse refers to salvation beyond the grave, after given an amazing display of God’s predestination to salvation in the opening verses (Eph 1:3-6), salvation by grace through faith (2:8-9). After death comes the judgment (Heb 9:27). All things will be put under His feet and they already are actually— since all authority is given to the Lord Jesus (Mt 28:18), He already is Lord both of the...