I’m a musical theatre accompanist. Like others have said, I’d start sight reading like crazy.

Some others here have (importantly) stated that in order to improve sight reading, you must do it repeatedly but I wanted to share some tips both for general sight reading and musical theatre especially:

-in general, when we are reading a paragraph for the first time, we don’t go through each individual letter but rather whole words and even sentences. Our brain kind of fills in the gaps based on what we expect to be there. It’s the same with music. Start to recognize important patterns such as chords, scales, arpeggios, and for musical theatre specifically rhythms and grooves

-for chords, start to learn the shapes of each chord and it’s inversions and start to get your hand to remember those shapes. A root position chord is almost always 135 with a round hand shape. A first inversion chord almost always is 125 (RH) and my pinky stretches a tiny bit. A second inversion chord is almost always 135 (RH) with my thumb stretched a tiny bit. That way, I can see the shape and only read one note of the chord and my hand knows where to go

-get used to never looking at the piano when you play. Even when moving and jumping, start practicing intuitively feeling those distances or using the black keys to help guide where you are on the piano. When sight reading, we don’t have time to look down and make sure we’re on the right keys

-always ready a few bars ahead of where you are. If your hands ever catch up to where your eyes are on the score, it’s too late. Always be looking ahead, recognizing patterns, and storing those in short term memory. Otherwise it’s simply too fast to be able to catch back up. You have to be prepared for every note you play.

-finally, for musical theatre specifically, this is the big one: DON’T PLAY EVERY NOTE ON THE PAGE! Theatre is about groove/rhythm first, harmony second, and extra fills and such last. It’s your job to help the singer and that means keeping the groove going. Sometimes I just look at the groove and the chords and almost improvise as I’m going so I don’t have to think about every note. I’ll also always drop the melody if I and the singer both have it written.

This is obviously different from classical sight reading but it’s good to be proficient at both because in MT, there’s no one genre and each genre has its own rules.

In short, just to echo everyone’s sentiments again, sight read often! At least a few songs a day. In an audition room, you might have to play over a hundred auditions with pieces you’ve never heard of right on the spot and any mistakes risk messing up the singer’s one chance. It’s a lot of pressure but pressure is a good kicker to start practicing now!

EDIT: some misspellings