Not always. Article 37 of the UK GDPR makes a DPO mandatory for public authorities and for organisations whose core activities involve large-scale processing of special category data or large-scale monitoring. Independent schools are not public authorities, so whether the duty applies depends on your processing. In practice, most schools we speak to appoint one anyway, because a named DPO is what parents, insurers and inspectors expect to see, and it gives the governing body a clear line of accountability.