Green’s Dictionary of Slang

unicorn n.

[the image of the unicorn’s protruding horn]

1. a cuckold; also as adj. [play on horn n.1 ].

[UK]Dekker Wonderfull Yeare 134: The unicorne cobler . . . being over head and eares in sleepe . . . softly out-steales sir Paris, and to Helenaes teeth [taste] prooved himselfe a true Trojan.
[UK]Dekker & Webster Northward Hoe IV i: This traine was laid by the baggage herself, and Fetherstone, who [...] makes her husband a vnicorne.

2. a coach drawn by three horses, two abreast and one in the lead; also attrib.

[UK]Grose Classical Dict. of the Vulgar Tongue.
[UK]M. Edgeworth Belinda (1833) 322: Let me drive you out some day in my unicorn.
[UK]Lex. Balatronicum.
[UK]Egan Grose’s Classical Dict. of the Vulgar Tongue.
[Aus]G.C. Mundy Our Antipodes I 139: Mr. Seale’s best [...] four horses (unicorn at least!).
[UK]Hotten Dict. of Modern Sl. etc. (2nd edn) 242: unicorn a style of driving with two wheelers abreast and one leader ? termed in the United States a spike team.
‘Some Road Slang Terms’ in Malet Annals of the Road 389: 1. Of Horses Pickaxe team or unicorn...Three [i.e. horses in a team].
[Aus]Bulletin (Sydney) 30 Aug. 24/2: Twenty couples and one ‘unicorn leader’ made up the team. [...] The ‘unicorn’ man [...] had even less ‘purchase’ on the chains than his comrades. His hands were free, but a rope pulled round his waist, and was fastened to the end of the chain. [...] [T]he wretch harnessed as solitary ‘leader’ could not relax his exertions for a second without being found out.
[UK]J. Ware Passing Eng. of the Victorian Era 255/1: Unicorn carman (L. Streets’, 19 cent.). Driver of three horses harnessed tandem.

3. a woman and two men/two women and a man in league for criminal purposes.

[US]Matsell Vocabulum.
[UK]Farmer & Henley Sl. and Its Analogues.
[Aus]Crowe Aus. Sl. Dict. 91: Unicorn, two men and one woman stealing in company, a style of driving with two wheelers abreast and one leader.

4. a second, bisexual woman who will join a heterosexual couple for intercourse [joc. ref. to the trad. unlikelihood of meeting the mythical creature].

Twitter 7 Dec. 🌐 Lot of men on Tinder currently ‘looking for a unicorn’ which I thought was slang for a bisexual woman who will shag them and their girlfriend and not expect any emotional involvement from either.

SE in slang uses

In phrases

go the complete unicorn (v.)

to make a display of oneself.

[UK]‘Cuthbert Bede’ Adventures of Mr Verdant Green (1982) I 129: Mr Bouncer ‘went the complete unicorn’ for the last time in the term, by extemporising a farewell solo to Verdant which was of [...] an agonising character of execution.
[UK]Essex Newsman 8 July 2/7: Going the Complete Unicorn at Colchester [...] Henry Byford, a labourer, was charged with being drunk and disorderly.