You still need an annual whole-practice appraisal and a connection to a designated body or a suitable person. Independent practitioners usually arrange this through private appraisal providers or membership organisations. Plan the route before resigning, because an unplanned gap in appraisal is painful to repair.
Inside the NHS, appraisal happens to you. Outside it, you build it: a designated body connection (several private providers and membership bodies offer this), an appraiser, and a portfolio that covers your aesthetics scope, volumes, CPD, complications and patient feedback. None of it is difficult, all of it needs arranging in advance.
Nurses have the parallel NMC version (450 practice hours, 35 CPD hours, confirmer), which a solo practice meets with some deliberateness. Both are covered in the NHS guide.