The brushes are usually held in place by a coil spring that pushes against the top of the brush, this is lifted up to insert the new brush?
If you have a problem finding originals, try Helwig Carbon, either for replacements or something you can use in place of.
In a real pinch, ones that are close can be shaved or sanded down to the required size, care must be taken however to avoid movement or slop in the brush holder.
That appears to be a extraordinary long commutator to have only one brush set, especially for a spindle motor, I would have expected to see two brushes, side-by-side.
Al.
CNC, Mechatronics Integration and Custom Machine Design
“Logic will get you from A to B. Imagination will take you everywhere.”
Albert E.