K'Mpec died in the year 2367.

Gowron died in the year 2375.

The entire length of Gowron's reign was just eight years.

'I want you to discover which one of them has killed me. Gowron or Duras. Find the assassin.' - k'mpec

'The Klingon who kills without showing his face has no honor. He must not lead the Empire.' - k'mpec

'Such a man would be capable of anything. Even war with the Federation.' - k'mpec

In the episode “Reunion” of Star Trek: The Next Generation, K'mpec the Chancellor of the Klingon High Council is poisoned and suspicion falls on the two rival claimants to be his successor: Duras and Gowron.  By the end it is pretty heavily implied that Duras was the poisoner, and Ronald D. Moore has confirmed in interviews that it was him, but it is never definitively established in the episode itself.  In the years since, there’s been a pretty sizeable section of the fandom that thinks it was Gowron after all.

Before his death, K'mpec had stated that a Klingon who could kill in such a manner as poison, which is viewed as cowardly and dishonorable by the Klingons, could stoop to any depths.  He specifically mentions that they might even seek to start a war with the Federation, despite the two powers being allies for years at this point.  On the surface this points to Duras, who had appeared in the show previously and was shown to be coward and traitor on general principles, but as we see over the following 10 years of TNG and DS9 it also applies to Gowron.

In this episode, Gowron makes threats so blatant that they can barely be called “veiled” at all.  One of which directly implies that he had a hand in killing K'mpec.  By the end this seems to be dismissed by the main cast as bluster, but only because their focus on Duras keeps them from investigating Gowron further.

Afterwards, we see Gowron re-writing the story of how he came to power to downplay the role that the Federation played in his ascent.  It’s one thing to embellish and exaggerate his own deeds -- that’s an established part of Klingon legend and storytelling -- but to flat-out deny that somebody else even helped (In effect “stealing” their honor) is something else altogether.  It also parallels Duras’ own history and why he was viewed as dishonorable in the first place: Duras lied to cover up the actions of his traitorous father and shifted the blame to somebody else, and now Gowron lies to deny the actions of somebody else and shifts the glory to himself.

Going to the longer term and more specifically relating to K'mpec’s warning, Gowron eventually does start a war with the Federation.  In an underhanded way as well.  Instead of directly renouncing their alliance or challenging the Federation directly, as an honorable Klingon would, he first tries to drag the Federation into his conquest of Cardassia.  He neither consults or explains his plans, but expects the Federation to just let him do whatever he likes and actually help him along the way.  When they refuse to go along with him, pointing out all the flaws in his actions, Gowron accuses them of betraying him.

As the Dominion War drags on, Gowron also tries to have rivals -- even potential rivals -- killed off so they won’t challenge him.  Back in “Reunion”, one of the key pieces of evidence pointing towards Duras as the poisoner was that one of his soldiers was a suicide bomber that attacked a meeting where he and Gowron were both in attendance.  They decided that Duras was attempting to kill Gowron (And perhaps Picard as well), and maybe he was, or maybe Gowron was just getting started early and trying to put the blame on Duras.