Is it ethical if I do paid tutoring in a subject taught by my department?
Given that you are not involved in the delivery of the course (and thus have no incentive to teach it badly in the hope that people will approach you for private tuition), and you are not party to privileged information (e.g.: examination questions), there is no ethical issue here.

That said, if you work for the university full-time, you may want to check your employment contract, in case it had some sort of exclusivity clause prohibiting you from taking on any freelance or consultancy work (that said, employers do not generally enforce such a clause unless your freelancing/consultancy interferes with your capacity to carry-out your duties to the employer).