Adam Clarke on Acts 9:23

And after that many days were fulfilled - What follows relates to transactions which took place about three years after his conversion, when he had come a second time to Damascus, after having been in Arabia. See Gal 1:17, Gal 1:18. What he did in Arabia we know not; he probably preached Christ in different Jewish synagogues; but with what fruit we are not told. St. Luke, who could not have been ignorant of this part of his history, passes it over in silence; and any assertion, at this distance of time, Relative to his employment in Arabia for those three years, must be both foolish and impertinent.