Green’s Dictionary of Slang

relieving officer n.

also R.O.
[SE relieving officer, an officer appointed by a parish or union to administer relief to the poor]

one’s father.

[UK]Lancaster Gaz. 24 Oct. 5/6: Many gents [...] had no father, but they possessed ‘a governor’ or ‘a relieving officer’ .
[US]Letters by an Odd Boy 162: A a male parent — not unwilling to meet our wants — [is] ‘a relieving officer.
[Aus]Clarence & Richmond Examiner (Grafton, NSW) 18 Jan. 4/6: It is grand ‘form’ [...] to call [...] a father a ’relieving officer’.
[UK]E.C. Grenville-Murray People I Have Met 227: Now the relieving officer, or, for brevity’s sake, the ‘R.O.,’ was a term of endearment which the Honourable Felix, in common with other young noblemen and gentlemen at Eton, applied to his father.