On his father's death in 1799 he was appointed to succeed him as deputy to the registrar of deeds of Ireland, a sinecure office held by his uncle George Ogle since 1784.
Between 1817 and 1819 he argued against the abolition of the office of registrar of deeds (for which as deputy he received substantial fees) before the commission on the Irish courts of justice.
A high Tory and member of the Orange Order, his contemporaries commented on the contrast between the violence of his political opinions and the mild-mannered way in which he expressed them.
Moore did not contribute to the costs of the petition to overturn the election, and after its success declined to stand at the resultant by-election, instead formally proposing Lord Ingestre as candidate.
As a staunch Tory deprived of a political career, Moore attempted to secure the appointment of one of his sons as assistant registrar in 1835, after Sir Robert Peel returned to government, but was rebuffed.