This quote is part of the final comments by King Claudius at the end of Act 4. Laertes has stormed back to Elisinore demanding vengeance for his father's murder. Claudius has been kept VERY busy in these scenes with Laertes trying to first calm him down, then deflect responsibility from himself to Hamlet, commiserate over the insanity of Ophelia, convince Laertes to hatch a plot against Hamlet, and finally console the bereaved Leartes upon hearing that his sister had drowned herself. Claudius probably heaves a huge sigh of relief that he survives the act at all!
When Laertes first returns to Elsinore he lays the blame for his father's death more on Claudius than Hamlet, because while Hamlet did the act, Claudius should take some responsibility for keeping control of his seemingly crazy step-son. Laertes is furious when he first enters the room and wants to blame anyone who will listen, but Claudius assures him that "I am guiltless of your father's death / And am most sensibly in grief for it." He no more than delivers these words, when Ophelia, who has lost her mind from grief, enters the room in a clear state of madness. She talks to each person in the room, but makes little sense. Laertes is devastated to see his sister like this, and blames Hamlet for his part in destroying her through his treatment of her as well as the fact that he killed their father. Again, Claudius has to talk Laertes down with assurances that he is as upset as Laertes over this turn of events and says that "we shall jointly labor with your soul / To give it due content." He means that he will do whatever he can to make Laertes feel that justice has been served in this case. Claudius agrees that Hamlet will have to pay with his life. What is ironic is that this is EXACTLY what Claudius wants. He is already actively planning to have Hamlet killed while doing official business in England.
Claudius tries to explain why he didn't take a stronger hand with Hamlet -- that he was beloved of the people and of Gertrude, but assures him that things will change now. He no sooner delivers this promise when a messenger arrives with the note from Hamlet announcing that he has returned in secret from England. Laertes is aroused to anger again and boldly states that this news "warms the very sickness of my heart." Leartes agrees to be "ruled" by Claudius and go along with a plan against Hamlet as long as "you [Claudius] will not o'errule me to a peace." He wants vengeance, not concessions.
As the scene progresses, Laertes and Claudius hatch their plan to draw Hamlet into a sword fight where they will have a poisoned and sharpened sword as well as a cup of poisoned wine. Just when Claudius can think he can be pleased with his fine manipulation of Laertes to do Claudius's "dirty work," news arrives that Ophelia has committed suicide. This pushes Laertes to fury again, but Claudius calms him down by reminding him that they have a fool-proof plan to bring Hamlet to justice. Claudius feels very lucky that he has been able to control and maneuver Laertes into this plan by the end of Act 4, but it has been a lot of hard work and smooth talking that let him achieve those ends. The ultimate irony is that all of these events have been set in motion because of Claudius's murder of King Hamlet in the first place!