Acts 19:14 (ESV) refers to "Seven sons of a Jewish high priest named Sceva" who were practicing exorcism at Ephesus. While some translations refer to Sceva as a "chief priest," the Greek word ἀρχιερέως is the genitive of ἀρχιερεὺς which refers to Caiaphas at John 11:51 (ESV) as "high priest." As there was only one high priest, located at Jerusalem (an making allowance for Annas being prematurely retired by the Romans - a sort of high priest emeritus), how could a Jew of the dispersion be designated as a high priest?
Seven sons of a Jewish high (ἀρχιερέως) priest named Sceva were doing this.
(Acts 19:14 ESV)
The high priests "...comprise in addition to one holding the high priestly office, both those who had previously discharged it and although disposed, continued to have great power in the State, as well as the members of the families from which high priest were created, provided that they had much influence in public affairs." [ἀρχιερεύς-archiereus]
Some commentaries suggest the title may also have been applied to the heads of the 24 courses of priests (1 Chronicles 24). Although as Ellicott notes the title may have been one [falsely] claimed and part of the "imposture." [Acts 19:14] This may the best explanation as Sceva is Latin and it is unlikely a Levitical priest would be given a Latin name.
On the other hand, the text does not actually say the man was named Sceva:
And there were seven sons of one Sceva, a Jew, and chief of the priests... (KJV)
As there was only one high priest ...
The Greek word translated here as high priest is ἀρχιερεύς (archiereus). In over half of its occurrences in the New Testament, it is in the plural, not singular. For example:
And when he had gathered all the chief priests and scribes of the people together, he demanded of them where Christ should be born. (Matt 2:4, KJV)
Saying, Behold, we go up to Jerusalem; and the Son of man shall be delivered unto the chief priests, and unto the scribes; and they shall condemn him to death, and shall deliver him to the Gentiles (Mark 10:33)
And he taught daily in the temple. But the chief priests and the scribes and the chief of the people sought to destroy him (Luke 19:47)
Then came the officers to the chief priests and Pharisees; and they said unto them, Why have ye not brought him? (John 7:45)
The following account comes from a 14th century Christian source that was supposedly drawing from Jewish sources (perhaps Josephus):
King David, seeing that the descendants of Aaron had multiplied and attained such a great number that it was impossible for all of them to serve in the temple at one time, divided them into twenty-four courses or divisions. Each division would perform its office one after the other so that all the priests could serve in the temple. David also chose the most honorable persons from among them and established them as chiefs over the others so that each course had its own principal priest. As there were more than five thousands priests in each division, lots were cast in order to avoid dissension in respect to precedence, and these determined which priest with his division would serve on the first week, the second, the third, and so on, until the twenty-fourth week. Each course received its assignment according to lot.*
* The Great Collection of the Lives of the Saints, Vol. 1 (tr. from the Slavonic; Chrysostom Press, 1994), pp.98-99.