10th division had no captain when Urahara instated as captain of the 12th division and the post (most likely) had yet to be filled by the time Urahara was exiled. In vol 36 during the "turn back the pendulum" mini-arc set 110 years prior to the start of the series during the time leading up to Urahara's inauguration the captains discuss the present state of affairs. They mention things such as 11th company's captain Kenpachi (the 10th i.e. the one before Zaraki) is slacking off which explains his absence throughout the arc, that 12th company's previous captain was promoted hence why Urahara has been appointed as captain and that 10th company's captain has died. All active captains were summoned twice during the arc, once during the inauguration of Urahara and then at the climax of the arc when Captain Commander Yamamoto is responding to the disappearance of 9th division's investigation team, in both instances squad 10 lacked a delegate, this strongly implies the post is vacant. We do not know when Isshin Shiba (later Kurosaki) was appointed captain of 10th company but we do know when he left the post, 20 years prior to the start of the series and 90 years after Urahara was exiled. This is expanded upon in chapter 529 onwards which shows Isshin investigating a mysterious series of shinigami deaths, fighting a prototype arrancar, getting backstabbed by Aizen, meeting Masaki, giving up his soul reaper powers and settling in the human world.