There can be little doubt that "diligencia" is near the top of the list of Spanish words most hated by translators. This is mainly because it is given so many different meanings. In this case one has to note that the words are those of the notary, and what he is saying is that he will add the information to the public deed he is issuing by means of a "diligencia" once it has been received. Those of you who like me eke a living out of translating Spanish deeds will know that often the deed will end with a page addded subsequently headed "DILIGENCIA". So how is it to be translated? I truly hope someone can come up with an authoritative answer, but I have got away with translating it as "additional procedure or notarial act" because that is what it is.

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Note added at 19 horas (2024-04-27 16:22:04 GMT)
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The notarial glossary entry posted below clearly states that a notarial "diligencia" is an addition to a preexisting document. Note also the use of "constar" as in the asker's source text.

diligencia f. Acta donde consta la forma y circunstancias en que se ejecuta un acuerdo o decisión judicial. Asímismo, hay diligencias notariales, en las que se hace constar en un documento ya preexistente una actuación posterior en el tiempo.

D - Glosario de términos notariales - Notariado