The noun gentrification designates the process whereby the character of a poor urban area is changed by wealthier people moving in, improving housing, and attracting new businesses, typically displacing poorer inhabitants in the process.

In this acceptation, gentrification was coined by the German-born British sociologist Ruth Glass (1912-1990) in London: Aspects of Change. Centre for Urban Studies Report No. 3 (London: MacGibbon & Kee, 1964) [Introduction, page xviii]:
—as quoted by Neil Smith in The New Urban Frontier: Gentrification and the revanchist city (London: Routledge, 1996) [page 33]:

One by one, many of the working-class quarters of London have been invaded by the middle classes—upper and lower. Shabby, modest mews and cottages—two rooms up and two down—have been taken over, when their leases have expired, and have become elegant, expensive residences. Larger Victorian houses, downgraded in an earlier or recent period—which were used as lodging houses or were otherwise in multiple occupation—have been upgraded once again…. Once this process of “gentrification” starts in a district it goes on rapidly until all or most of the original working-class occupiers are displaced and the whole social character of the district is changed.

However, I have found an isolated early occurrence of gentrification, designating the process of turning into a person of high social rank, in the following letter, by ‘a mechanic’, published in The Brisbane Courier (Brisbane, Queensland, Australia) of Saturday 25^th November 1865 [Vol. 20, No. 2,443, page 5, column 3]:

NORTH BRISBANE SCHOOL OF ARTS.
TO THE EDITOR OF THE BRISBANE COURIER.

Sir,—Some weeks ago I stated through the Courier some of the reasons why the above institution was not more frequented by us mechanics of Brisbane. I observed a letter by a member of the School of Arts soon after mine appeared, stating […] that the mechanics did not take sufficient interest in the Brisbane School of Arts; and quoting from Lord Brougham and the late Mr. Cobbet, showing that the mechanics ought to keep the management of such institutions in their own hands.
Now I have some reason to doubt the desirability of having the management wholly in the hands of mechanics in any community, and still less in a colonial community, where mechanics are ever moving, some to other parts of the colony, following their callings; others acquiring property put on an air of “gentrification” and pass into the uppertendom *, and become aristocratic and conservative.

* The noun upper-tendom is from:
– the noun upper ten, originally upper ten thousand, designating the upper classes, the aristocracy;
– the suffix -dom, used in the sense of state, condition, rank, dignity.

The earliest occurrences that I have found of the noun gentrification—in the sense of the process whereby middle-class people take up residence in a traditionally working-class area of a city—are as follows, in chronological order:

1-: From the Daily Mirror (London, England) of Thursday 23^rd March 1972 [No. 21,212, page 15, column 4]:

A WORD of hypnotic nastiness has entered the language. In parts of London—Camden, Fulham and Battersea—where middle-class opportunists are moving in to snap up working class houses the process is being referred to as “gentrification.”

2-: From Speculators cash in on housing grants, by Laurence Marks, published in The Observer (London, England) of Sunday 16^th April 1972 [No. 9,429, page 2, column 4]:

A LARGE proportion of Government house improvement grants in Inner London is going to commercial developers who are using the money to help finance highly profitable property speculation.
This is the conclusion of studies carried out by several housing organisations.
They claim that the grants, so far from alleviating the housing shortage, are helping to destroy communities in the twilight areas, increase homelessness and boost house prices.
[…]
Mr Bernard Kilroy, research officer of the Notting Hill Housing Trust, […] points out that the prices and rents after conversion are beyond the reach of families with moderate or low incomes.
‘The national stock of housing has not been increased in the short run since a house which was about to become unhabitable would not qualify for a grant anyway, but would be pulled down,’ he says.
‘All that has happened is that the stock of housing available to the lower income groups has diminished and that attractive to the middle class has increased.’
And this process of gentrification—the march of the carriage lamps and the mauve doors across Inner London—is even more destructive of communities than redevelopment, where the local authority is at least responsible for rehousing the dispossessed.

3-: From a letter to the Editor, by Bruce Birchall, of the Notting Hill Theatre Workshop, published in the Kensington News and Post (London, England) of Friday 21^st July 1972 [No. 7,080, page 37 [or 13?], column 3]—Anthony Perry was the Director of the North Kensington Amenity Trust responsible for the land under the Westway motorway:

Your columns have been consistently sympathetic to an analysis that local working-class people are being displaced from the area by the effect of improvement grants, and the middle-classes are moving in fast. “All out by 1980” is one prediction.
By 1980, the amenities under the Motorway should be well under way to completion. But it will not be the present population who will be here to enjoy them.
The new amenities at the bottom of the road will only add to the attractions of the area for the middle-class invasion, and arguably will speed it up.
Until Antony [sic] Perry takes a position on the gentrification of the area, his promises are worthless.

The earliest occurrence that I have found of the verb gentrify—meaning to renovate housing—is from A Palace of Art (London: Victor Gollancz Ltd., 1972), a novel by the Scottish author John Innes Mackintosh Stewart (1906-1994)—as reprinted in 2012 by Stratus Books Ltd., Looe, Cornwall [page 4]:

Chevalley […] fell silent as he studied Nudd Manor.
It was apple-pie all around and spick-and-span all over, as such places in the Cotswolds tend to be. Pitched at a just remove from the village over which it presided, its finely proportioned intricacies of buffy stone nevertheless gave the appearance of having generously broadcast the influence of their own high amenity. There were several other houses of some consequence and an equal antiquity, and in point of up-keep each might have been described as very consciously up-keeping with the others. Everywhere the lawns were velvety, the shrubs clipped, the trees (like not a few of their owners) assisted by unobtrusive surgery to preserve shapeliness into old age. The humbler dwellings—or those in which there had been some original intention of housing the industrious poor—were well-groomed rather than neat, and their little gardens had been gentrified as effectively as had their low parlours, large-ovened kitchens, and garret bedrooms hazardous to the heads of all save dwarfs.