*Merriam-Webster's Eleventh Collegiate Dictionary* (2003) gives a straightforward summary of the etymology of *trinity*:
>**Trinity** n {M[iddle] E[nglish] *trinite*, fr. A[nglo-]F[rench] *trinité*, fr. L[ate] L[atin] *trinitat*-, *trinitas* state of being threefold, fr. L[atin] *trinus* threefold} (13c) 1 : the unity of Father, Son, and Holy Spirit as three persons in one Godhead according to Christian dogma} ...
What this summary tells you is that the word *Trinity* appeared in English from Middle English in the thirteenth century; that it was derived ultimately from the Latin word for "threefold," and that its original meaning in English was the religious one indicating the three-in-oneness of Jesus/God/Holy Ghost.
The earliest instance that a Google Books search for "Holy Trinity" turns up is from [*Articles agreed upon by the Bishops, and other Learned and Godly Men, in the last Convocation at London, in the year of our Lord 1552. To root out the Discord of Opinions, and establish the Agreement of TRUE RELIGION. Published By the Kings Majesties Authority, 1553.*](https://books.google.com/books?id=O_BYAAAAcAAJ&pg=PA2&dq=%22holy+trinity%22&hl=en&sa=X&ved=0ahUKEwiHgbb76_LOAhUDKiYKHTipCXwQ6AEIJDAC#v=onepage&q=%22holy%20trinity%22&f=false) (1553):
>*Of Faith in the **Holy Trinity**.*
>There is but one living and true God, and he is everlasting, without body, parts, or passions; of infinite power, wisdom, and goodness, the Maker and Preserver of all things both visible and invisible. And in unity of his God-head there be three persons, of one substance, power and eternity, the Father, the Son, and the Holy Ghost.
The king was Edward VI, in what proved to be the final year of his reign.
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***Update: A look at early matches for 'Trinite' and an earliest match for 'holy Trinite'***
In hopes of finding an earlier instance of "Holy Trinity," I ran a Google Books search for *Trinite*, the predecessor word in Middle English to *Trinity*. The most interesting result was a concordance to the A, B, and C versions of William Langland, [*William's Vision of Piers Ploughman*](https://en.wikipedia.org/wiki/Piers_Plowman), the famous medieval allegorical poem, which Wikipedia reports was written circa 1370–1390.
The concordance turns up several dozen matches for *Trinite* [or *trinite*], and it finds even more matches for *holy* (particularly in the combinations *holy chirche* [or *churche* or *kyrke* or *kirke*], *holy gost* [or *goste* or *goost*], and *holy writ*, but also occasionally in the forms *holy day* [or *dayes* or *daies*], *holy men*, and (once each) *holy Seintes* and *holy euen*. But there is only is only one instance in which *holy* and *Trinite* appear in the same line, and in that case *holy* modifies *goost*:
>So grace of þe holy goost þe grete myȝl of þe Trinite
Virtually all instances of *Trinite* in *Piers Ploughman* are preceded by *þe*. This proves nothing about whether some contemporaries of William Langland used the term *holy Trinite*; but it does provide fairly strong evidence that in the late 1300s *holy Trinite* was not a set phrase in Langland's part of England the way that *holy chirche*, *holy gost*, and *holy writ* were.
In Tarjei Park, "[Reflecting Christ: The Role of the Flesh in Walter Hilton and Julian of Norwich](https://books.google.com/books?id=ucfbRfBFf-MC&pg=PA87&dq=%22trinite%22&hl=en&sa=X&ved=0ahUKEwiKpu3Y6fPOAhUE7mMKHfItD0w4FBDoAQhMMAg#v=onepage&q=%22trinite%22&f=false)," in *The Medieval Mystical Tradition in England: Exeter Symposium V* (1992), the academic author reproduces several quotations from Julian of Norwich's *Revelations of Divine Love* (ca. 1395), including one that comes close to "holy Trinity":
>For the **Trinite** is God, God is the **Trinite**; the **Trinite** is our maker and keeper, the **Trinite** is our everlasting lover, everlasting ioy and blisse, be our lord Iesus Christ. And this was sewed in the first and in all; for where Iesus appereith the **blissid Trinite** is understood, as to my sight.
Most of Julian's mentions of *Trinite* are unmodified, but the last one, *blissid Trinite*, comes close to *holy Trinite*. Still her choice of *blissid* in place of *holy* as the adjective suggests that "holy Trinite" was not a set phrase in her own mind.
An 1841 edition of [*Lyttleton, His Treatise of Tenures, in French and English*](https://books.google.com/books?id=_1i_opjDyWoC&pg=PR35&dq=%22trinite%22&hl=en&sa=X&ved=0ahUKEwiKpu3Y6fPOAhUE7mMKHfItD0w4FBDoAQhFMAc#v=onepage&q=%22trinite%22&f=false) includes in its introduction the text of Thomas Lyttleton's will (written not later than 1481), which includes this provision:
>Also I bequeth my gode littel mass book and gode vestment with the apparel to an auter of the same sorte of vestments which were my moder's, and also a gilt chalës, I geve them to the **blessed Trinitë**, to the use and occupation of my chapel of Frankley in honour of our said most **blessyd Trinitë**: inasmuch as the said chapel of the **blessyd Trinitë** and an aulter thereof is halowed in the worship of the said **blessyd Trinitë**, for to have masse songen there on **Trinitë Sunday** and other high festivals and other days to the pleasure and honour of our said most **blessyd Trinitë**.
This is Julian of Norwich's preferred phrase with a vengeance (especially as Lyttleton charges that the Lord of Frankley must meet the terms of this bequest and obligation "as he will answer to the blessed Trinitë").
However, a search of the Early English Text Society's collection, [*Songs, Carols, and Other Miscellaneous Poems, from the Balliol Ms. 354, Richard Hill's Commonplace-book*](https://books.google.com/books?id=JSVLAQAAMAAJ&pg=PA28&dq=%22trinite%22&hl=en&sa=X&ved=0ahUKEwiKpu3Y6fPOAhUE7mMKHfItD0w4FBDoAQgqMAI#v=onepage&q=%22holy%22&f=false) (1907), whose contents Hill gradually collected over the period 1508–1536, finds one crucial match. Searches within the book yield 43 pages matches for *holy* and 12 pages with matches for *Trinite* [or *trinite* or Trynite]—and one pair is in combination:
>**Vnto the Trinite.**
>**Holy Trynite**, blessed & eterne,
>Ever regnyng *in* p*ar*fight vnite,
>Whose power, Lord, no thynk may deserne,
>Ne þe joyes no*m*bre of thy dignite,
>Thy grace eu*er* in eche necessite
>Be my ocowr, my fawt*is* to redresse,
>& w*i*t*h* thyn hond, Lord, eu*er*y day me blesse!
Google Books is very poor and finding matches from before the late 1500s, owing to the relative scarcity of early books in its database and to OCR problems with early English fonts. So there are surely some and perhaps many earlier instances of *Holy Trinity* in published English than the earliest one it finds (from no later than 1536). But there is at least some reason to doubt that *Holy Trinity* was already in widespread use in England as *holy Trinite* in the late medieval period, as well as some reason to suppose that during the period 1390–1490 the wording *blessed* [or *blissid*] *Trinite* may have been in more common use.