Yes you need to have a Trados Studio license, the online editor comes with Trados Studio 2019 and Trados Studio 2021.

Having a Trados Studio license or product would help on your work and also will ensure you can take on jobs requiring a CAT tool. However at the beginning, for learning purposes you can also benefit of the free 30 days trial of Trados Studio

https://www.trados.com/products/trados-studio/free-trial.html

If this question relates to the profile you have in Trados Live Team as a user, then no you do not need to specifically own a licence.  When you are added as a user you will be able to draw a licence by signing into the Trados Live Team account you have been added to and will be able to use it for your project.  As long as you area user in that setup you will be seen as a translator (if that was the role you were given).

You can read a little about roles here:

https://docs.rws.com/795494/866196/trados-live-team/users-and-groups/user%2520types%252C%2520roles%252C%2520and%2520personas