According to Article 6 of the GDPR, the processing of personal data is only lawful if and to the extent that at least one of the following applies:
the data subject has given consent to the processing of his or her personal data for one or more specific purposes; processing is necessary for the performance of a contract to which the data subject is party or in order to take steps at the request of the data subject prior to entering into a contract; processing is necessary for compliance with a legal obligation to which the controller is subject; processing is necessary in order to protect the vital interests of the data subject or of another natural person; processing is necessary for the performance of a task carried out in the public interest or in the exercise of official authority vested in the controller; processing is necessary for the purposes of the legitimate interests pursued by the controller or by a third party, except where such interests are overridden by the interests or fundamental rights and freedoms of the data subject which require protection of personal data, in particular where the data subject is a child.
In this case, the Spanish employer would most likely depend on the legal obligation of the employer as the lawful basis for sending the personal data of its employees to the national tax authority. This is because the employer is subject to the tax laws and regulations of Spain, which require the employer to report the income and deductions of its employees to the tax authority on an annual basis. The employer must comply with this legal obligation, and the processing of the employees' personal data is necessary for this purpose. The employer does not need to obtain the consent of the employees, as consent is not a valid basis for processing personal data where there is a clear imbalance between the data subject and the controller, such as in the context of employment. The employer also does not need to rely on the legitimate interest of the public administration, as this is not a specific purpose for which the employer is processing the personal data, but rather a general interest that may be served by the tax authority. The employer also does not need to invoke the protection of the vital interest of the employees, as this basis only applies in situations where the processing is necessary to protect someone's life, such as in a medical emergency. Reference: Article 6 GDPR - Lawfulness of processing - General Data Protection Regulation (GDPR), Lawful basis for processing | ICO, Legal obligation as a lawful basis for processing personal data under the GDPR, [Consent in the employment context | ICO], [Vital interests | ICO]