This is a quotation from the Royal Charter issued by Charles V in 1544, founding the Consulado de Sevilla. It is quoted in Antonio de Capmany, Código de las costumbres marítimas de Barcelona [...] hasta aquí vulgarmente llamado Libro del Consulado (Madrid, 1791), p. 161.
https://books.google.es/books?id=CA79u3KTKwcC&pg=RA1-PA161&l...

The particular passage quoted here is part of a petition, in response to which the Seville Consulado was founded, addressed to Charles V by one Ciprián de Charitate on behalf of the international trading community of Seville: "los mercaderes de todas las naciones que residen en la dicha ciudad de Sevilla", explaining that there were "consulados" in other Spanish cities where merchants resided, such as Burgos, Barcelona, Valencia, but not in Seville.

Here's what these words mean:
"Prior: [...] el que es cabeza del Consulado establecido en Andalucia (como los que habia antiguamente en Burgos y Vilváo) y es para la disposicion del despacho de las Flotas y Galeones [...]"
"Consul: En algunas partes de nuestros Reinos [...] los dichos Mercaderes tienes sus Cónsules, que hacen y administran justicia en las cosas de mercaderías"
"Consulado. Se llama assimismo el Tribunal que antiguamente en algunas Ciudades de España estaba destinado para juzgar de las cosas tocantes al comercio: y oy existe para el mismo efecto solo en lo que pertenece al comercio de Indias"
(Definitions from the first RAE dictionary of 1721-39.)

These words are the same in English. In his Spanish-English dictionary of 1706, under Cónsul, John Stevens writes:

"There are now two Consuls of the Corporation of West India Traders at Sevil, who, together with the Prior, regulate all matters relating to that Trade."

And in The Rule Establish'd in Spain, for the Trade in the West Indies, by José de Veitia Linage (1623-88), translated by Captain John Stevens (not sure if this is the same person), these same terms, prior and consuls, are used, as they are in plenty of other more modern sources. This source calls the Consulado the "Consulship Court", or just "Consulship".
https://books.google.es/books?id=sk0Y3hV30r0C&pg=PA73&lpg=PA...

But what of "Universidad"? It doesn't mean university. The word had other meanings, and the relevant one (quoting again from the first RAE dictionary) is:

"Significa assimismo la Comunidad, Junta, o Assamblea, en que están adscriptos muchos para algun fin"

The sense of it, really, is "corporation". But in English the word "university" was also used in this sense, which is now obsolete. Here's the OED on "university":

"4. a. A body or company of persons associated together for some purpose. Obs.
[...]
b. A body or class of persons regarded collectively; esp. an aggregate of persons forming a corporate body or society, a corporation. Obs.
[...] 1755 N. Magens Insurances II. 40 The Prior and Consuls..of the University of the Shippers and Merchants..of this City of Seville"
http://findwords.info/term/university

So then in rendering this sixteenth-century quotation you could, if you like, use "university" in this sense, which was current in sixteenth-century English, adding "corporation" in square brackets to make the sense clear. I think that's what I would do.

But also there's a small but important error in the quotation: it's not "por via de la Universidad de Prior y Consules", but "por via de Universidad de Prior y Consules", with no article. So it's not a proper name, an institution; it means "by way of an universidad", not "the universidad". It's not a proper name; it's a generic name. And "de Prior y Consules", likewise, is not a name, the "university of prior and consuls"; it means "of prior and consuls" in the sense of "endowed with a prior and consuls". It's a descriptive phrase for the kind of "universidad" that the merchants didn't have in Seville but needed, and got in 1544.

--------------------------------------------------
Note added at 3 hrs (2016-01-18 23:29:52 GMT)
--------------------------------------------------

I didn't get round to saying that the initial capitals don't mean anything; they don't mean it's a name. Significant generic nouns are liberally capitalised in older Spanish texts.

--------------------------------------------------
Note added at 3 hrs (2016-01-18 23:33:25 GMT)
--------------------------------------------------

And by the way, for "consulado" you could borrow "consulship" from Stevens' translation, but I would add "mercantile court" for clarification, just as I would add "corporation" to clarify the obsolete sense of "university".

--------------------------------------------------
Note added at 4 hrs (2016-01-18 23:55:40 GMT)
--------------------------------------------------

On reflection, you might prefer to dispense with "university" in this obsolete sense, as most readers will probably misunderstand it, and simply put something like this:

"because they do not have a consulado [consulship or mercantil court] to deal with their affairs by way of a corporation with a prior and consuls [...]"