Hm, I’m going to take a stab at this…someone correct me if I’m wrong!
St. Andrew founded the church at Byzantium…so I believe his successor is His All Holiness, Bartholomew I, the Ecumenical Patriarch of Constantinople.
Since St. James the Greater was leading the church in Jerusalem, his successor is probably His Holiness Gregory III Laham, Melkite Patriarch of Antioch and all the East, Alexandria and Jerusalem.
St. John, however does not have a direct successor…as someone who currently sits in his see, which is defunct. There has been no titular head of this see since 1992.
gcatholic.com/dioceses/former/t0680.htm
St. Philip…I’m not sure about. I can assume though that his see is defunct and may not have even a titular head now.
St. Bartholomew preached to the Armenians…and so his successor is His Holiness Karekin II Surpreme Patriarch and Catholicos of All Armenians–head of the Armenian Orthodox Church
or, it could be His Beatitude Nerses Bedros XIX Tarmouni, patriarch of the Armenian Catholic Church. That depends on who you ask…
St. Thomas founded the church in India, but it is unclear who is his successor. I would wager that it is either
-His Beatitude Mar George Alencherry Major Archbishop of Ernakulam-Angamaly
(Syro-Malabar Church)
-or any of the heads of the various other “St. Thomas Christian” churches in the area.
St. Matthew apparently preached to the Ethiopians so his successor is the head of the Ethiopian Orthodox Tewahedo Church, which currently is vacant.
St. James the Lesser was, according to tradition martyred in Egypt…but St. Mark founded the Church in Egypt.
St. Jude, also, does not have a direct successor that I know of…but that depends on his ancient see.
St. Simon the Zealot, also must have had an ancient see that either has a current head or a titular head.
As for St. Paul, I really have no idea. It depends on whichever church he was first a bishop of!
Though, we need to remember that all bishops are successors to the apostles through the line of consecration and succession. The ones i listed are only the /direct/ successors, meaning they occupy the see of any given Apostle!