With Sir Arthur Chichester, who became Lord Deputy of Ireland in 1604, he lived on terms of intimacy, and several small offices of state, with a pension granted 5 November 1607, were bestowed on him in his youthful days.

On 13 March 1611–12 James I wrote to the Lord Deputy confirming his grant of the fort and land of Mountnorris to Annesley "in consideration of the good opinion he has conceived of the said Francis from Sir Arthur's report of him".

He was nominated on a committee of the Irish privy council appointed to investigate charges of injustice preferred against Falkland by the Byrne Clan, who had held land in County Wicklow for centuries.

[1] In 1633 the formidable Sir Thomas Wentworth, afterwards Earl of Strafford, became Lord Deputy, and Mountnorris soon discovered that he was determined to insist on the rights of his office far more emphatically than Falkland.

Although they were related by marriage, Wentworth disliked Mountnorris from the first as a gay liver, and as having been long guilty, according to popular report, of corruption in the conduct of official duties.

Fresh charges of malversation were brought against him in 1635, and, after threatening to resign office, he announced that all intercourse between the Lord Deputy and himself was at an end, and that he would take his case to the king personally.

[1] Wentworth was now resolved to crush Mountnorris, and on 31 July following obtained the consent of Charles I to inquire formally into the Vice-Treasurer's alleged malversation and to bring him before a court-martial for the words spoken at the dinner in April.

The only real justification for Wentworth's conduct, however, lies in the fact that he had obviously no desire to see the sentence executed; he felt it necessary, as he confessed two years later, to remove Mountnorris from office, and this was the most effective means he could take.

On the report of the privy council's committee of inquiry he was stripped of all his offices, but on 13 February 1635–6 a petition to Strafford from Lady Mountnorris, which was never answered, proves that he was still in prison.

In the petition, she pleaded eloquently with Strafford to remove his "heavy hand" from her dear husband, and appealed to the memory of his beloved second wife Arabella Holles, who was her cousin.

A committee of the Long Parliament had begun at the close of 1640 to examine his relations with Strafford, and on 9 September 1641, a vote of the commons declared his sentence, imprisonment, and deprivations unjust and illegal.

The declaration was sent up to the House of Lords, who made several orders between October and December 1641 for the attendance before them of witnesses to enable them to judge the questions at issue; but their final decision is not recorded in their journals.