Staunchly loyal to the Repoublic, and what would later become the Galactic Empire, Governor Tarkin, otherwise ranked as Grand Moff, was a military leader, bureaucrat, and strategist. His devout and unwavering loyalty often gained favor with the Emperor, and would land him one of the most important positions of the Empire. The Death Star. Ironically, however this position would also be his tomb.
Tarkin is a military leader first, and during the Clone War, he saw the Jedi Order as an obstacle in ending the conflict decisively. He has been often noted as saying that the Jedi, as peace keepers had no place in a military setting and should be sidelined to allow for competent soldiers and generals to lead the Republic to victory. Though, despite his apparent distrust in the Jedi Order, there was one Jedi that he had actually befriended, and learned to respect. That being Anakin Skywalker.
As the Empire rose from the ashes of the Republic, the Jedi Order was wiped out. And despite the carnage and mass executions, Captain Tarkin held no remorse or care for their deaths. In his view it was the end of an ancient religion. And he did his best to snuff out any remnants of that order. When word of a Jedi would arise, he would be the first to dismiss any claims. Saying that the Jedi Knights were all wiped out in the purge, and that anyone claiming to be one was no more than common rabble trying to stir up old wounds.
Even when the evidence of a Jedi was right in front of him. Tarkin remained completely skeptical. The only time he accepted that a Jedi had in fact survived was when his top associate, Lord Vader believed that former Jedi General Obi-Wan Kenobi had somehow ended on the Death Star. Tarkin would attempt to move all stations to stop, capture, and presumably execute the general, only to be stopped by Vader himself while favoring a more risky plan to find the rebel stronghold.
Wilhuff Tarkin has zero tolerance for failure and incompetence. When any Imperial fails to perform their duties, and makes a habit of poor choices, he opts for that soldier's summary execution, allowing for more competent soldiers to take the fallen's place. A philosophy that determines that the weak to die off in favor of the strong, for a lasting Empire.
The same can be said of any rebels and traitors to the Empire. At one point, Grand Moff Tarkin ordered the complete destruction of a peaceful world once held by the Imperial Senate to be utterly vaporized by the Death Star's main weapon. If only to demonstrate the Empire's resolve to end the Rebellion. Though his plan would backfire as this only rallied the Rebellion into a fierce fighting force resulting in the Battle of Yavin, where Tarkin would finally meet his end.