Slow Left Hand

Also known as the "One-handed Piano Player".

This is what happens when an actor who doesn't know how to play piano is cast as a pianist—and doesn't get proper instruction on how to fake it. They sit at the keyboard—sometimes with their hands thoughtfully obscured by the cameraman's choice of angle—and pretend to play. But while their right hands dance all along the full length of the ivories, their left hands hardly move—if they move at all—and nothing the cameraman can do short of pointing the camera elsewhere can hide it.

In extreme cases, neither hand moves, or neither moves in a manner that in any way corresponds to the music.

Meanwhile, the music on the soundtrack is obviously played by real pianist who knows how to use both hands.

The equivalent can be found displayed by actors trying to fake being guitarists: their left hand remains motionless or nearly so on the neck of their guitar (frequently clamped onto it as though it were a handle), while their right hand aimlessly strums the strings, often out of synch with the music they're trying to mime to.

This can be avoided with the proper use of a Talent Double. Sometimes.

Subtrope of Artistic License Music. Related to Special Effect Failure. A potential opposite trope is The Cast Showoff. Not to be confused with Red Right Hand, The Crawling Hand or The Left Hand of Darkness. Definitely not to be confused with Slowhand, who is a very good musician, thank you very much.

Examples of Slow Left Hand include:

Film

It may come as a surprise, but Chico Marx was occasionally subject to this trope. A self-taught pianist, his left hand technique was somewhat limited, and at times vanished entirely when he had to mime playing to a pre-recorded soundtrack. (A need, conscious or unconscious, to hide this may have contibuted to the comedic moves he made with his right hand while playing.) A good example of his Slow Left Hand is visible in A Night at the Opera—see this clip.
In the first scene of the 2005 film of Pride and Prejudice, Mary is allegedly playing the piano, but does not appear to even touch the keyboard!
Farley Granger as Phillip in Alfred Hitchcock's 1948 film Rope plays piano during the course of the film, but the movements of his hands rarely correspond to the music he's supposedly playing.
Dooley Wilson in Casablanca is a classic example—Sam's hand movements almost never match up to what he's playing. For the most part his right hand moves around more or less in the correct neighborhood, but there are times where it's obviously wrong—for instance, during the first time he plays "As Time Goes By" for Ilsa there's a rapid treble run where his right hand should have ranged up and down the keyboard—but it doesn't move an inch.
During the first "White Christmas" sequence in Holiday Inn, Bing Crosby's character Jim Hardy is allegedly playing the song on a piano, but his left hand is all but motionless through much of the song.
Carefully averted in Deliverance. Billy Redden, who played Lonnie, couldn't actually play the guitar that his character uses to perform his side of the famous "Dueling Banjos". A skilled player was hired to replace his left hand on the neck of the instrument, with shots composed and camera angles chosen to hide the fact that while Redden might have been strumming the guitar with his right hand, another man's hand was performing the hard part of playing a stringed instrument, so that it looked real.
When Clark Hill is playing guitar and singing in 2016's Brave New Jersey, his left hand is motionless on the fret board.

Live-Action TV

An aversion can be found in the 2009 episode episode of Bones "The Plain in the Prodigy", in which the camera lingers lovingly on the actor portraying "Levi" as he genuinely—and expertly—plays the piano.
Kelsey Grammer's fake piano playing is actually pretty convincing in Frasier - but if you look closely, you can see that it's 'dubbed'.