Built-up tartar can and should be removed before, during and after orthodontic treatment. If a clean is needed before treatment, it is best done at least a few days before the braces or aligners are fitted, to give the gums time to heal. While you are wearing braces or aligners, there is no reason not to have tartar removed and your teeth polished. This can be done by your orthodontist, the advantage being that they can take out the archwires if you have braces and polish the braces themselves more thoroughly. A general dentist or a periodontist can also do the cleaning. After orthodontic treatment, if needed, cleaning can be done straight away when the appliance is removed. Polishing the teeth with bicarbonate of soda (air polishing) is not recommended more than twice a year.
This answer is for general information. Your own case needs an examination by an orthodontist.