Translation:The secretary does not have confidence in us.
That sounds like a hyper-correction to me.
When "trust" is a noun, you "have trust in" or "put trust in" someone/something. - "The secretary does not have trust in us" (which is probably a better translation of this sentence).
When "trust" is a verb (as it is in the English translation of this exercise), you don't need the "in" - "The secretary does not trust us". It is sometimes used in infinitive constructions ("to trust in the Government"), but to use it between two people sounds archaic at best to me, though maybe it's just a US English thing.
The verb “trust” can be used either transitively or intransitively. When used transitively, the “in” isn’t needed; when used intransitively, the “in” is needed. The “to have faith” intransitive meaning is the first definition of the verb “trust” given in the OED (and thus the oldest meaning), so perhaps it remains in current use only in North America — although some Irish examples also exist, e.g. the statements “Trust in us to help guide your financial future” here and “More than 200 businesses trust in us.” here (I have no connection with either firm).
Not when used with the preposition ag - tá muinín ag X as Y
But you can use i in a construction like Is beannaithe an fear a chuireann a mhuinín sa Tiarna - "Blessed is the man who puts his trust in the Lord".
Here's an example from the 2006 Annual Report of An Bord Pleannála
Measaim gur léirigh an tOireachtas a mhuinín sa Bhord trí fhreagracht a chur ar an mBord as nós imeachta toilithe pleanála amháin a fheidhmiú do thionscadail bhonneagair straitéiseacha -
"I consider that the Oireachtas expressed confidence in the Board by assigning responsibility to the Board for operating a single planning consent procedure for strategic infrastructure projects."