"I am wanting a new job this year."
Translation:Tha mi ag iarraidh obair ùr am-bliadhna.
Correct, as bliadhna is feminine. Am is some sort of preposition. It is often used to make adverbs of time: an-dè, an-diugh etc. The form am is simply what you get before a b. It looks like the word for 'in' which doesn't make much sense at first. 'On' makes more sense as we are used to 'on Tuesday'. But there are two points to make here.
1. The two have fairly similar meanings and are often interchangeable. We see that in arguments on this site such as https://forum.duolingo.com/comment/36486475?comment_id=36486476 and the two were interchangeable in some languages (e.g. in in Latin and and ἐν in Ancient Greek).
2. We still use 'in' with some times such as 'in 1983' so there is no logical reason for not using it for this year as well.
Mark says it is generally the definite article but your comment clearly disproves it, as does the fact that this does not make sense. However it does sound like the definite article and that is thought to be the reason that we use the in Scots, e.g. the now, the day etc., simply a mis-translation of the Gaelic an-dràsta, an-diugh etc.