Do all gene drives spread?

Gene drives spread through mating between individuals that carry the drive system and those that don’t (wild type). All gene drive systems have the potential to spread to some extent. The defining characteristic of gene drive is preferential transmission to the next generation, and this will result in the gene drive element increasing in frequency (spreading) within the interbreeding population of the target species. Some gene drive technologies are designed with temporal or spatial limitations on the degree of anticipated spread, and therefore the gene drive is expected to remain more localized.

For more information:
https://www.who.int/publications/i/item/9789240025233