"in the right direction" is correct and usable in written English. You can use this phrase when you are talking about making progress or making a positive change. For example, "I'm glad to see that this project is moving in the right direction."
We're moving in the right direction".
"Steps in the right direction".
"It's going in the right direction".
I'm headed in the right direction".
It does move in the right direction.
But surely in the right direction.
There are steps in the right direction.
She's in the right direction again.
This agreement moves in the right direction.
We started out in the right direction.
A brave step in the right direction.
Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.
Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com