At Gloucester's castle, Regan confers with Oswald, Goneril's servant, who's en route to deliver a message from Goneril to Edmund. Regan gets the news that Albany's forces have set forth (the battle is on), but it seems like Goneril is the one inspiring them to do bloody battle, at least more so than is Albany, who seems to be more or less hesitant.
The conversation shifts to Edmund, whom Regan now has the hots for, as his glossy new title is likely as attractive as his unforgivable villainy. Also, Regan's bed has been cold ever since her husband died.
Regan suspects that Goneril might be in for a piece of Edmund pie, so she presses Oswald for more information; she'd especially love to see the letter he's carrying.
This would be all well and good, but it's clear Regan and Goneril are enemies, and Oswald knows where his bread is buttered.
As he refuses to give up the information, Regan speaks plainly that although her sister might "love" Edmund too, she (Regan) should really get to marry him, as something of a consolation prize for her husband who died yesterday.
Regan peevishly gives up on trying to worm herself into Oswald's confidence. She does, however, give him a token that she hopes he'll pass on to Edmund on her behalf, once Oswald finds Edmund to deliver Goneril's letter.
Finally, Regan informs him that there's a reward for killing Gloucester. Oswald says he's eager to knock off the man in exchange for money.