Captain James Stewart served as Superintendent of Edinburgh City Police until 1842, when he was succeeded by Captain William Haining, a former Metropolitan Police officer. 

William, the son of a farmer, John Haining, was born near Dumfries in 1802.  It is believed that he was a merchant seaman before joining the Metropolitan Police in London as a Constable in August 1833.  He served in “A” Division (Whitehall/Westminster), becoming a Sergeant in 1834, and an Inspector in November 1836.  In the latter part of his service he was based at Gardners Lane Police Station, one of two Police Stations on “A” division, the other being Great Scotland Yard. 

William married Hannah Robinson Mather on 12th January 1841 in Westminster, and they had three children, William John (born 1841), Charles Orries (born 1845) and Joseph Frederick (born 1847). William was paid a £300 salary by the Commissioners of Edinburgh City Police, and in addition to his post as Superintendent of Police, he also held the post of Procurator Fiscal. 

According to the Edinburgh Post Office Directory of 1844 the police command structure was as below with Richard Moxey succeeding William Haining and then in turn Thomas Linton succeeding Richard Moxey.

POLICE ESTABLISHMENT.
The Sheriff of the County, the Sheriff-substitutes,
the Four Bailies of the City, and Judges.
William Haining, Superintendent of Police.
Richard John Moxey, Clerk of Police.
“Wm. Eerr, Alex. R. Christie, Andrew Crawford,
and Thomas Linton, Lieutenants.

He and his family lived at police quarters in Buccleuch Place. William suffered from severe ill health in 1847, which is attributed to the poor conditions in Edinburgh at the time.  Sickness and starvation were commonplace, and sanitary conditions were very poor.  Diseases such as cholera, typhus, typhoid, and influenza afflicted the population, and William is thought to have suffered from one of these illnesses.  He died in London in March 1848, having taken a leave of absence from Edinburgh due to his ill health, and was buried in Westminster.

(Most of the text provided by RHaining, to whom I am grateful)