Tarkin was, arguably, highest ranked official with any degree of operational independence in the Empire - various imperial advisors like Sate Prestage and Ars Dangor technically outranked him, but their power was entirely through their direct connection to Palpatine. He had sufficient authority to give Darth Vader orders in ANH and was granted massive authority to make huge decisions regarding Imperial policy, such as ending the Clone program and replacing them with Stormtroopers. His military doctrine, fatally flawed though it was, also achieved dominance in the Imperial military. Note that his primary competitor in this was Thrawn, and Tarkin beat him in the political arena, soundly. From the perspective of the kind of people who consider the Empire a horrifying monstrosity, yes, Tarkin is terrible, but from the perspective of the people ideologically inclined to support such a regime, he's very close to the ideal. The military brass and the regional governors would support him.
Chancellor is the obvious move. Tarkin can get himself appointed to the Senate easily: his family controls the Senate seat represented by the Seswenna Sector which is controlled by his homeworld of Eriadu, which his family de facto rules. Using the existing title to maintain continuity of government and convince the politically disengaged that this isn't a big deal is logical. Now, I suspect that Tarkin would, if he claimed power for any significant length of time, grant himself some sort of grandiose military title like 'Galactic Admiral' or something and preferentially go by that in public, but he'd still maintain the Chancellor title.Originally Posted by Errorname
After all, Tarkin's not a Sith Lord, and even if he was able to arrange for Order 66 to go off or to purge the Jedi through some other means, he'd be very vulnerable to Jedi assassination. In order to maintain power, he'd have to make sure that the Jedi consider assassination worse than the alternatives. This reality applies to anyone who isn't a Force user controlling the galaxy unless they have some other kind of failsafe.