docker-compose run container before other container stop
If you mean make sure that container A does not execute and then exit then no.  Docker containers will stop if the container crashes or if the main process exits.

However, if you are attempting to run container B and it is dependent on container A, I think the depends_on flag may be what you are looking for.  This will allow you to ensure that service B will run after service A is started.  However, you may need to add something to service A that ensures that it is ready before attempting to connect to it (e.g. a database).