I got to level 70 persuasive and I don’t know how to get a better profession. Please tell me if you know how :).
You can get a tier 1 profession on various of the faction opportunity cards (e.g. become a campaigner on the church or the revolutionaries cards) as long as you meet some not-especially-stringent requirements.
If the option to take on a profession requires that you don’t already have one, you can resign from your current profession by choosing to Write A Letter, in your Lodgings.
Do check first though, as some professions require you already be a certain profession when you do the action.