Firstly, how do you know that material design is the next step?
This is basic UX process for an in-life product. You need to reach out to users and find out how they are using it. You need to reach out to the stakeholders/product owners to find out if the business needs are being met - then you need to try to align those two sets of data.
Once you have done that you should have a clear idea of what the goals of any redesign/revamp should include. You could prioritise them to ensure you fix the most damaging problems first and leave the "nice-to-have" things for when there is more time/budget to improve your product.
If, at this point, Material will solve some/all of your problems, then you're ready to go. However, Material is just a visual language and NOT a UX panacea. You will still need to find and solve the UX problems if you want to see a significant improvement for your product.
This is the point where you start to come up with ideas and test them out (preferably on users if you can get them in) with prototypes.
Once you think you have conquered the problems you can put the solutions into a final design and hand it over to the developers to build.
If you're working in Agile then you can do most of this a small bit at a time. Completing the full cycle of discover (find the details of the problem), design (create and test something to solve the problem), and deliver (create the final design deliverables for the fix) for each detail you want to fix.
Although you will still need to run the initial requirements discovery (users needs, business needs, prioritisation) all on it's own to make sure you capture everything you can and prioritise it correctly.