If you are an EU citizen, you will need:

1. NIE (Foreigner Identity Number).
2. Digital certificate.
3. Social Security number.

In addition, if your are planning to stay in Spain for more than 90 days, you must apply for the European Union Citizen Registration Certificate.

If you are a non-EU national, in order to formalise the employment contract you must have a valid residence and work permit that allows you to start an employment relationship with the university.
If you do not have such permit, the university will apply for the initial residence permit for research provided for in the Law 14/2013, of 27 September, to support entrepreneurs and their internationalisation. In the same procedure you will be assigned a Foreigner Identity Number (NIE), in case you do not have one yet. This permit is issued by the Large Companies and Strategic Collectives Unit (UGE-CE) and there are two possible scenarios at the time of application:

• You are not living in Spain: Once the residence permit has been granted, you must personally apply for the national researcher's visa at the Spanish Consular Office corresponding to your place of residence. The permit will not be valid without this visa. Once in Spain, you must apply for the Foreigner's Identity Card (TIE) within 1 month after entering the country. *Remember that it us compulsory to apply for the TIE if your stay is longer than 180 days.
• You are already living in Spain holding another type of residence or stay permit that does not authorise you to work, or on a short stay, with or without a visa: In this case, once the residence permit for research has been granted, it is not necessary to obtain a visa; you must apply for the Foreigner's Identity Card (TIE) within 1 month. 

Note: when foreign public documents are submitted for the application, they must be previously legalised or, if applicable, apostilled, and must be translated by a sworn translator authorised by the Spanish Ministry of Foreign Affairs.

Once you have the residence permit and, if applicable, the visa, in order to formalise the employment contract, you must also have an digital certificate and a Spanish Social Security number.

Since there is a change of employer, the circumstances under which you were granted the permit are also changing. Therefore, in order to start the employment relationship with the university, you must apply for a new initial residence permit.

The permit holder must apply for renewals in due time, as long as the circumstances remain the same. In other words, to be able to renew the permit, you must still be employed at the university. You should apply for renewal preferably within 60 calendar days before the expiry date but, you are also entitled to do it within 90 calendar days after the expiry date. 
Applications for renewal of authorisations must be submitted electronically, using a digital certificate, at the electronic office of the Ministerio de Inclusión, Seguridad Social y Migraciones.
It is compulsory to use the application forms for residence authorisations of Law 14/2013 and to pay the fee using the form 038. To pay the fee, please tick the box "autorización de residencia renovada" in the taxable event "movilidad internacional" from section 7. 
To certify that you are still employed at the university, you must request by email (pasinvest@uv.es) the supporting document from the HR Service PAS-Research.

Once your contract ended, if you wish to remain in Spain you can apply to the Large Companies and Strategic Collectives Unit (UGE-CE) for a 12 months extension of your residence permit to seek for employment. To do so, you must provide proof of completion of your research activity, health insurance either public or private and sufficient financial resources. This extension does not authorise you to work (Article 72.9 of Law 14/2013).

You must consider that the residence permit for research issued by the Large Companies and Strategic Collectives Unit (UGE-CE) is granted on the basis of your employment contract with the University of Valencia. Therefore, you can maintain and renew such permit while the employment relationship with the UV is in place. Any modification of the admission circumstances, including the termination of your contract with the university, must be communicated by you to the UGE-CE within 30 days (as stated in the Seventh Additional Provision of Law 14/2013).