Many cellists are afraid of playing in the high register. Without the reassuring opposition of thumb and fingers that we have in the neck position, the left hand can feel adrift and uncertain.
For a lot of advanced players, the pressure of performance anxiety can make thumb position fraught with hazards, even when things have gone just fine in the practice room. Heightened tension...poor intonation...difficulty shifting...even difficulty getting from note to note within one position.
Luckily, these problems can be greatly ameliorated by shaping the left hand rationally. These surprisingly simple exercises can make playing in thumb position easier because they allow the hand to do one of the things it does most naturally: making a fist.
Step 1: Make your left hand into a loose fist, with your thumb resting gently alongside the fingers.
This is how it should look from the other side. Your fingers will look slightly "sloped," just as they will in thumb position on the cello.
Step 2: "Unfurl" your fist and rest it on the string, with your thumb on the A and D harmonics. Note that your hand's shape is really not much different from a fist. All the knuckles of your fingers should be gently curved, but especially the base knuckles (i.e. the metacarpophalangeal joints).
Now, why should we keep those base knuckles curved? Don't a lot of cellists flatten their base knuckles in thumb position?
Yes, they do. Everyone's hand is different in terms of size, flexibility, strength, agility, and so on, and it takes every cellist time to figure out hand shaping that works.
But on many hands, flattened base knuckles in thumb position will make it very hard to move from note to note. That's why so many players find that their "top" knuckles (i.e. the ones at the proximal interphalangeal joints) buckle in thumb position, as in the picture below. While buckled knuckles may not matter so much in slow tempi, it's very cumbersome to try to play fast like this. What's more, it's hard to get the fingers to move independently, and they end up squished together or all stuck down at once.
By contrast, if you just keep those base knuckles curved, you'll find that you can sink your arm's weight into the pad of each finger as you move independently between them. You can use your arm's movement to move from finger to finger without having to alter your hand's shaping or angle very much.
If you move your thumb alongside your hand wherever you shift to, you'll find it easy to maintain a curve in your base knuckles. Many cellists execute a shift, but don't take their thumbs with them! This is like going on vacation without taking your suitcase.
Part of your daily fundamentals practice should be re-establishing good hand shaping in thumb position. You can do this by starting from the "fist" hand shape, then practicing getting from note to note in varying combinations of half steps and whole steps. The exercises on page 31 of Cello Practice, Cello Performance will help with building and maintaining this fluency.
Additionally, click on the links below to download free PDFs of exercises in tetrachords and one-octave scales in thumb position. I'm a great believer in killing two birds with one stone, so what I've tried to do with these exercises is to reinforce music theory principles (modal scales, non-diatonic scales) at the same time as building cello fundamentals. Happy practicing!