A meek middle-aged clerk has to escape a violent interrogation by a determined CIA agent who identifies him as the nation’s number one terrorist menace.

Q: “how can one pull off the promise of a twist without giving away the twist?”
A: For me, Genre is key and carries with it an inherent payoff for the viewer.
Check out this “The Sixth Sense” logline in your Thriller genre family:
“A psychologist struggles to cure a troubled boy who is haunted by a bizarre affliction – he sees dead people” [CREDIT: J GIDEON SARANTINOS].
Notice we have a protag, story goal, obstacles, and can envision three-acts, but one of the biggest twists in movie history [SPOILER ALERT! The psychologist is – a ghost] is not mentioned. Thus, I revert to my original statement of reviewing the Examples header link to help construct your story basics in a format where we/I can assist – then zhuzh up from there.

Take care.

That is indeed a correct logline for The Guilty, but it is not representative of the movie and its twists.

So my not-so-rhetorical question is how can one pull off the promise of a twist without giving away the twist?

I have not seen The Guilty but based on IMDB / Rotten Tomatoes the logline probably looked something like “When getting disconnected from a kidnapping call, an alarm dispatcher and former police officer must use his skills to rescue the woman and apprehend her kidnapper before it’s too late”
Concerning your question about your challenge, just start with your story's premise – then build from there. See Examples (top menu) to help construct – the goal is to get your logline in a state where the community can help.

Take care.