It depends on your definition of "apostle".
- a delegate, messenger, one sent forth with orders Thayers
is, lit., "one sent forth" (apo, "from," stello, "to send"). "The word is used of the Lord Jesus to describe His relation to God, Hbr 3:1; see Jhn 17:3. The twelve disciples chosen by the Lord for special training were so called, Luk 6:13; 9:10. Paul, though he had seen the Lord Jesus, 1Cr 9:1; 15:8, had not 'companied with' the Twelve 'all the time' of His earthly ministry, and hence was not eligible for a place among them, according to Peter's description of the necessary qualifications, Act 1:22. Paul was commissioned directly, by the Lord Himself, after His Ascension, to carry the Gospel to the Gentiles.
"The word has also a wider reference. In Act 14:4, 14, it is used of Barnabas as well as of Paul; in Rom 16:7 of Andronicus and Junias. In 2Cr 8:23 (RV, margin) two unnamed brethren are called 'apostles of the churches;' in Phl 2:25 (RV, margin) Epaphroditus is referred to as 'your apostle.' It is used in 1Th 2:6 of Paul, Silas and Timothy, to define their relation to Christ." *
[* From Notes on Thessalonians, by Hogg and Vine, pp. 59-60.] -Vines-
If you use the word apostle as did Peter in Acts 1:22, then the last apostle is Matthias. He was of the twelve.
Beginning from the baptism of John, unto that same day that he was taken up from us, must one be ordained to be a witness with us of his resurrection.
For Peter, at this time, an apostle was an eyewitness.
Paul, some three years later, was called by God to preach to the gentiles, but so were others to whom Paul points. It is as if the idea of an apostle was shifting from an eyewitness of Christ's ministry to the Jews to a faithful witness of the gospel to all peoples, yet one who is called of God..
Salute Andronicus and Junia, my kinsmen, and my fellowprisoners, who are of note among the apostles, who also were in Christ before me. Rom 16:7
But other of the apostles saw I none, save James the Lord's brother. Gal 1:19
Which when the apostles, Barnabas and Paul, heard of, they rent their clothes, and ran in among the people, crying out, Acts 14:14
So, was Paul the last apostle? The bookends of Christ's specifically called apostles as eyewitness spread from James to John, sons of Zebedee, first and last apostles to die. But as apostles called to faithfully spread the gospel to all peoples, Paul and the others like Barnabas were also apostles during that period.
While there were eyewitness apostles and let's say "special" apostles overlapping that time from from ascension to John's death, we may presume to conclude that the office of apostle ended with John. We do this as there is no known record of other apostles specifically endowed with incredible gifts of the Spirit as apostles were wont to show when they preached the good news.