Agus iad ar ais sa phríomhroinn, an Dún a thug an taispeántas is fearr Ultach inné nuair a tugadh lán a léinte do Thiobraid Árann i nDúrlas.

Since they are back in the main division, Down gave the best Ulster display yesterday when......????....to Thiobraid Árann in Thurles.


I'm also unsure about the use of 'agus' here at the start of the sentence.

Agus iad ar ais - Now that they are back

tugadh lán a léinte do - literally: they got the fill of their shirts (I presume Down won convincingly?)

tugadh > one gave the fill of their shirts, the fill of their shirts was given (tugadh is the impersonal form of "thug", the past of the verb "to give", tabhair)

Agus iad ar ais sa phríomhroinn,

When you front a phrase like this to form an introduction, it is not uncommon to use "agus" here with the strength of As or Now that. Because what you are saying is that the subsequent action is taking place in the same context as the introductory phrase is true.

So both the following AND the introduction are true at the same time.

It is a great trick to avoid an overly complex main sentence. You're moving in this case something that adverbially qualifies the verb "thug" and are changing it to an a proper adverbial clause that is placed in the front simplifying the main clause and giving it emphaisis.

The sentence is actually ill-formed and would be better
as :

Inné agus iad ar ais sa phríomhroinn, thug an Dún an taispeántas Ultaigh is fearr, nuair a tugadh lán a léinte do Thiobraid Árann i nDúrlas.

Unfronting the adverbial phrase

Thug an Dún atá ar ais sa phríomhroinn an taispeántas Ultaigh is fearr inné, nuair a tugadh lán a léinte do Thiobraid Árann i nDúrlas.

Could also be phrased :

Ar ais sa phríomhroinn dó, is é foireann an Dúin a thug an taispeántas Ultach is fearr inné nuair .....

It is a question of emphasis, balance, clarity, rythm as to which phrasing one would use.

For example using the copula IS/BA it is possible to bring forward several elements to give them emphais.

Chuaigh mé go Doire inné.

Is mise a chuaigh go Doire inné.
Is go Doire a chuaigh mé inné
Nach inné a chuaigh mé go Doire.

The first emphasis is on who went, the second on where, the third on when.