I think Clare’s declaration of “My turn” should make for a fairly easy and believable transition without Frank.
I would think this would be a good time for his transplant to fail, fatally…
Also known for playing a character named “Kevin Smith,” who is somewhat less taciturn.
Joan Severance rolls over, looks at Ken Wahl and says “I just had the strangest dream about Mel as president”.
Or eaten by a malevolent oil slick on the planet Vagra II.
Assassinated by a madman trying to impress Kevin Spacey.
Frank Underwood continues to be in the series, but now he is played by Dick Sargent.
Actually I think it was more the age and willingness than the orientation.
Frank Underwood’s home planet? You mean K-PAX? 
I haven’t watched the Netflix version of House of Cards since the first season, but the original UK trilogy ended the character quite decisively. So Netflix might be able to copy that.
He gets hit by a car and someone comes along and breaks his neck to put him out of his misery.
Ooh! I get this one!
That’s what I was thinking (hoping) would happen eventually.
But surely he was cremated?
Well, yes, but you see him in an ashtray here, a bit of dust on the table there …
That joke took me longer than Detective Dave Kujan, you were already driving away in your Jaguar.
The coffee cup broke, it just said “Poof!”
He’s dead, with subtle hints growing less subtle that Claire may have had something to do with it. She needs her own house of cards.
How about there is mounting evidence that he is sexually abusing young men which leads to an indictment. Evidence is overwhelming so he goes off to prison after a plea bargain (a plea bargain so there needn’t be a trial which a TV show would want to have the actor appear in).
Art imitates life.
Maybe he’ll be killed off, and the last we see of him is his head in a box.
Delivered to the middle of the desert.
By Gwyneth Paltrow.
He could just walk upstairs, and never come back down.
The plot thickens…
Kevin Spacey Can’t Be Ousted from ‘House of Cards’ Over Allegations; No Morals Clause in Contract
Maybe just have him as a ghost in the background that nobody reacts to.
He never appears on-set (and in-scene) with any of the characters ever again.
Instead, he’s off to Fresno to care for his ailing mother (or whatever family relation you prefer, if it’s known his mother is already gone) and you only see him in brief split-screen telephone calls to other characters back on the main scene.
Until the contract is ended and you ditch him like a plague blanket.