A character considers taking the hand of a crush, sometimes reaching out, but decides not to. Standard way to show there is some attraction between the characters, at least one way, and usually it's a case of Unresolved Sexual Tension.
There are many ways this trope can come about. Perhaps the characters were interrupted by a ringing phone, a knock on the door or a thunderstorm. Perhaps the character is unsure how the other will react, and perhaps they are confused and unsure of their own feelings. Perhaps they remembered their deceased beloved one whom they had promised never to forget, or the thought of a Relationship Upgrade became just too frightening.
A Body Language trope.
- In the opening for Revolutionary Girl Utena, Anthy and Utena's hands reach to grab each other but slip away, a few seconds after an Almost Kiss. This symbolizes the unresolved romantic tension that lingers between the two for most of the series and also foreshadows a future point where Anthy is hanging off a cliff as Utena tries to save her.
- Chapter 142 of Kaguya-sama: Love is War has Kaguya trying to get Shirogane to hold her hand the day after their First Kiss, but he completely misinterprets the very unsubtle signals she's sending him. The fact that she's acting wildly out of character (combined with him suffering from a severe lack of sleep) didn't help matters.
- In Sweeney Todd: The Demon Barber of Fleet Street, Mr. Todd almost holds hands with Mrs. Lovett but doesn't.
- In the film version of Harry Potter and the Prisoner of Azkaban, Hermione and Ron touch hands in fear when first introduced to Buckbeak, but soon pull apart.
- Secretary: After E. Edward Grey first spanks his typist Lee for a typo in her letter, he puts his hand close to hers on a desk, and she briefly touches his fingers.
- In Harry Potter and the Order of the Phoenix, when Harry is on a date with Cho, he spends a long time working up the courage to hold her hand, but when he finally moves to do it, she pulls her hand away.
- In an episode of Star Trek: The Next Generation, William Riker and Deanna Troi (who used to be a couple) almost hold hands when it looks like their ship Enterprise is about to be fired upon.
- Sex Education: One recurring visual hint that Eric and his bully Adam are catching feelings for each other is their hands reaching out and touching, but without holding hands.
- "I Want to Hold Your Hand" by The Beatles: The upbeat melody implies the singer will touch his crush's hand and they will hold hands eventually.
- HoneyWorks's "Tokyo Summer Session" has Mio and Haruki go on a date, and both express their desire to hold the other's hand, but because they are too shy to even do that, Mio hides her hands behind her back, while Haruki hides his in his pockets.
- The Nostalgia Critic: The Nostalgia Critic tries to hold The Nostalgia Chick's hand in their awkward date, but chickens out and looks as if he's about to cry.
- The Dragon Prince: Callum arranges his hand, watching the shadows, so that he appears to be holding that of his crush, Claudia. She looks at him, and he quickly moves his hand away.