Peace was too important.
The alliance between the United Federation of Planets and the Klingon Empire, which began with the Khitomer Accord of 2293 (the result of Star Trek VI: The Undiscovered Country ) is perhaps the most important political alliance of the Alpha Quadrant. It ended a century of both active and implicit war between two of the biggest powers in the quadrant and brought a new and lasting stability to not only the Alpha Quadrant but also the Beta Quadrant (which the Klingon Empire extends into).
The Federation would not jeopardize this alliance for Riker's sake. At the same time, the Federation would recognize that Riker was officially an officer on the Pagh, and hence bound by the rules and laws of the Klingon Empire. His death would not have been a crime in the Klingon Empire, and hence not a crime in the Federation, which believes that its citizens must abide by the laws of other cultures when on their soil or in their space. (Wesley Crusher was almost allowed to be put to death for violating the laws of another world — see "Justice").
If there were any reprisals, they would have been on a personal level only. Riker's father, for instance, may have felt the need to exact revenge (although their relationship could not be described as "close" — see "The Icarus Factor").
In short, there would have been no official reprisal. The Federation would have at best asked for an inquiry into the death, likely with Federation observers present. A statement would have eventually been issued by the Klingon High Command that Riker had entered into the fight with full awareness that there was a high risk of death. The Federation Judiciary Body would have rubber stamped this, agreeing with the assessment and calling the death "regrettable". Federation officials would have issued a further statement, calling Riker something to the effect of:
"...a good man and a good officer, who died serving the interests of peace between the peoples of the Federation and the Klingon Empire".