Depends on what tutoring might mean.
You might use fridge magnets + postal route mailing or paid traffic from somewhere like Outbrain/Taboola/Gemini.
Tough to say with out extreme detail of tutoring you're offering.
Might be best for you to scan Clarify + hire people to assist you designing your marketing flow.
This is a great assignment. As a marketeer and designer who is also a teacher and professor, I would be excited working with you. I have helped different companies in education, from providers to in-company training to universities who would like to set up competence centers to serve businesses.
As a tutoring agency you have got two target groups. The customers who are looking for tutors, and the tutors themselves. You could simply create a promotional website explaining how to help both groups, or you could develop a more sophisticated business plan that evolves around presentation of the tutors in the best possible way, establishing initial contact via your site, streamlining the selection of the tutor and offering the business context for the tutors, setting up pay-out principles, charging and pricing models and the role of social media, reviews, et cetera. Perhaps you want to provide means for tutors and pupils to communicate with each other in between classes, share files, or give and look up excercises, marks and comments? And how about a planning tool for the classes and meetings?
Your business model and your business plan could be as comprehensive as you want it to be. And your marketing and online presence will follow suit.
For the design of your business model, we could have a short workshop; one hour is enough after which I we can collaboratively write a business plan. I will be guiding you, and the software I work with (Liveplan, it's paid but we can use my license) will help you a great deal as well.
Most of your marketing will happen online and it is up to you how you will further utilize the website to drive business (see my first ideas above). Depending on your decision how to go ahead online, I could stay involved and develop your web presence.
Anyways, you've got to be great for your tutors so you attract the best. This will - in the long run - give you the best business.
Let me know if you want to get in touch! A first call is for free.
Best of luck with the (future) business!