With reference to Jeeves, the perfect valet in stories by the English author Pelham Grenville Wodehouse (1881-1975), the adjective Jeevesian means: of, or relating to, or characteristic of, or resembling, Jeeves.

This adjective occurs, for example, in The Savoy reaches out for the stars, by Iain Hollingshead, published in The Daily Telegraph (London, England) of Wednesday 13^th October 2010 [No. 48,324, page 27, column 6]—“he” refers to Sean Davoren, “the head butler at the newly refurbished Savoy hotel in London”:

“You’d have to cut my head off before I told you anything indiscreet about any of our guests,” he says in a soft, slightly camp, Irish brogue.
Such Jeevesian levels of discretion are a shame because, if these walls could speak, they would have a thousand secrets to spill.

—Cf. also the adjective Jeeves-like, which means: resembling Jeeves.

The earliest occurrences of the adjective Jeevesian that I have found are as follows, in chronological order:

1-: From a review of Thank You, Jeeves (London: Herbert Jenkins Ltd., 1934), by P. G. Wodehouse—review published in the Manchester Evening News (Manchester, Lancashire, England) of Saturday 17^th March 1934 [No. 20,245, page 3, column 4]:

Bertram develops a passion for the banjolele. That starts the trouble. The love affairs of a millionaire’s daughter no longer dear to him although they were once engaged extends it. And when, after having his house burnt down, his face blacked, and his liberty taken away, he regains serenity by Jeevesian means you understand, if you did not know before, why Wooster cannot do without the genius of Jeeves and why the world cannot do without the genius of Wodehouse.

2-: From a review of Top Hat (1935), a U.S. musical film starring Fred Astaire and Ginger Rogers—review by Donald Kirkley, published in The Sun (Baltimore, Maryland, USA) of Tuesday 3^rd September 1935 [page 8, column 1]—Eric Blore (1887-1959) was an English actor:

Eric Blore, who made a minor reputation for himself in “Flying Down to Rio” and “The Gay Divorcée,” obliges with a comic portrait of a Jeevesian valet.

3-: From a review of Interference, a stage play by Roland Pertwee and Harold Dearden, performed by the Penzance Players at the Pavilion, Penzance—review published in The Cornishman and Cornish Telegraph (Penzance, Cornwall, England) of Thursday 7^th November 1935 [page 3, column 3]:

As Childers, C. Benson Crofts (the rector of St. Buryan) achieved that mechanical obsequiousness which stamps the cast of those who wait on Vere de Vere. He imparted much of his considerable skill to the portrayal of his Jeevesian character.

4-: From the Daily Mirror (London, England) of Monday 5^th October 1936 [No. 10,248, page 5, column 1]:

PERFECT BUTLER NOW HAS SCHOOL FOR THE SUPER GENTLEMAN’S GENTLEMAN
BY A SPECIAL CORRESPONDENT

THE secret of the Perfect Butler is to be found in the pads of his feet.
I learned this secret when I went to Bretson, superman’s man, late butler to Lord Bethell and the Marquis of Headfort, for a lesson on How to Buttle.
Bretson gave up buttling to open a school—the only one of its kind—where he could train raw youths in the art of manservantry.
[…]
Bretson’s first look when I presented myself was at my feet.
“The pads of your feet are the most important things about buttling,” Bretson began. “Once your arches fall the days of your stewardship are numbered.”
Thus I practised so that my presence—in true Jeevesian fashion—would be felt rather than seen or heard.

5-: From a review of Step Lively, Jeeves! (1937), a U.S. comedy film starring the English actor Arthur Treacher (1894-1975) as Jeeves—review published in the Moberly Monitor-Index and Moberly Evening Democrat (Moberly, Missouri, USA) of Saturday 1^st May 1937 [Vol. 18, No. 258, page 8, column 5]:

Treacher, as Jeeves, is the pivot of the plot of this comedy. The story, one that Wodehouse has never written, incidentally, deals with a pair of unsuccessful swindlers who try to convince the butler that he is a scion of nobility in order to use him as a “front” for their game. With convincing Jeevesian mastery—plus some of America’s best gangster methods—Treacher outwits the swindlers and restores himself to his own blissful, self-effacing position of servitude.

6-: From a review of Under Your Spell (1936), a U.S. comedy film starring the U.S. actor Lawrence Tibbett (1896-1960), the British-U.S. actress Wendy Barrie (1912-1978) and the English actor Arthur Treacher (1894-1975)—review published in the Acton Gazette and Express and West London Post (London, England) of Friday 18^th June 1937 [page 2, column 3]:

“Under Your Spell” […] gives you plenty of opportunities to hear that £50,000-a-year voice belonging to chubby Mr. Lawrence Tibbetts [sic]. Our own Korda-made * Wendy Barrie and Jeevesian Arthur Treacher are also well in the picture.

[* Alexander Korda (1893-1956) was a Hungarian-born British film director and producer who made major contributions to the development of Britain’s film industry.]

7-: The variant Jeevesean occurred in a review of Breakfast for Two (1937), a U.S. comedy film starring the U.S. actress Barbara Stanwyck (1907-1990), the English actor Herbert Marshall (1890-1966) and the English actor Eric Blore (1887-1959)—review published in the Washington Herald (Washington, District of Columbia, USA) of Saturday 16^th October 1937 [Vol. 15, No. 327, page 8, column 4]:

Mr. Blore, it is true, portrays another butler, and Mr. Blore has been cinematically buttling for some time. But in this case there is the exception—Mr. Blore is also a member of Mr. Marshall’s board of directors, which is a new wrinkle and puts him in a class to surpass any mere Jeevesean feat. Moreover, he is in practically every scene and is the chief projector of some of the subtler humor in the compound.