If you're looking for synonyms for "once a week," you might consider using phrases like "weekly," "every seven days," or "per week." Other options include "weekly basis," "once weekly," "once per week," "once every seven days," or "every week." There are also some more informal and colloquial expressions you could use, such as "once a week like clockwork," "week by week," or "on a weekly rotation." Depending on the context of your writing, you may want to experiment with different phrases to find the one that best suits your tone and intent.