cloak / klōk/ • n. an outdoor overgarment, typically sleeveless, that hangs loosely from the shoulders. ∎ fig. something serving to hide or disguise something: lifting the cloak of secrecy on the arms trade.• v. [tr.] dress in a cloak. ∎ fig. hide, cover, or disguise (something).

cloak a cloak is the emblem of St Martin of Tours.
cloak-and-dagger involving or characteristic of mystery, intrigue, or espionage; the term is recorded from the early 19th century as a translation of French de cape et d'épée or Spanish de capa y espada, relating particularly to dramas or stories of intrigue or melodramatic adventure, in which the principal characters are likely to be cloaked and armed with swords or daggers.

See also women beneath a cloak.

cloak sb. XIII. — OF. cloke, cloque, dial. var. of cloche bell, cloak :- medL. clocca (VII), perh. of Ir. origin (cf. CLOCK).
Hence cloak vb. XVI.