He seems to have done little to improve the abject condition of the Church of Ireland, although he was fully aware of it, remarking that he doubted that there were even forty Irish-born Protestants in the whole country.
A plan to strictly enforce the laws against recusants was vetoed by the Queen personally: she pointed out that by his own account, the vast majority of the population was Roman Catholic, and doubted that any good would come from provoking them.
He was, rather belatedly, made a member of the Irish Privy Council in 1585 (the delay was apparently due to the Queen's low opinion of him).
Due to his extravagant lifestyle, and the fact that his episcopal see produced little in the way of profit (the Queen had forbidden him to hold any other living in plurality), he accumulated very heavy debts, including one of £1000 to the Crown.
Although Fitzwilliam evidently did not share this high opinion of the Archbishop's services to the Crown, Anne's petition was granted, and the debt, despite its size, was written off.