Definition of "engage"

To interact socially.

1. (transitive) To engross or hold the attention of; to keep busy or occupied.  quotations  examples

   Quotations

   • Thus ſhall mankind his guardian care engage, / The promis'd father of the future age.

     1712 (date written), Alexander Pope, “Messiah. A Sacred Eclogue, in Imitation of Virgil’s Pollio.”, in The Works of Alexander Pope Esq. […], volume I, London: […] J[ohn] and P[aul] Knapton, H. Lintot, J[acob] and R[ichard] Tonson, and S. Draper, published 1751, page 40, lines 55–56

2. (transitive, intransitive) To draw into conversation.  quotations  examples

   Quotations

   • the difficult task of engaging him in conversation

     1850, Nathaniel Hawthorne, “Introductory”, in The Scarlet Letter, a Romance, Boston, Mass.: Ticknor, Reed, and Fields

   • Shapps refused to engage with the unions and claimed that the industrial disputes were nothing to do with him, despite controlling the purse strings.

     2022 September 21, Christian Wolmar, “Trevelyan must 'give a damn' and engage with the railway”, in RAIL, number 966, page 45

3. (archaic) to fascinate or win over (someone).  quotations

   Quotations

   • This humanity and good nature engages every body to him, so that when he is pleasant upon any of them all his family are in a good humour, and none so much as the person whom he diverts himself with: […]

     1711 July 13 (Gregorian calendar), [Joseph Addison; Richard Steele et al.], “MONDAY, July 2, 1711”, in The Spectator, number 106; republished in Alexander Chalmers, editor, The Spectator; a New Edition, […], volume II, New York, N.Y.: D[aniel] Appleton & Company, 1853, page 74

To interact antagonistically.

1. (transitive) To enter into conflict with (an enemy).  quotations  examples

   Quotations

   • a favourable opportunity of engaging the enemy

     1698-1699, Edmund Ludlow, Memoirs

   • Having failed to become the first warship to shoot down another planet, the fleet would then engage the Italian cruiser screen the next afternoon, with Sydney not scoring any hits on its opposite numbers but managing to damage an Italian destroyer.

     2018 December 12, Drachinifel, 5:45 from the start, in HMAS Sydney - Legendary fights with Angry Australians‎, archived from the original on 9 December 2022

2. (intransitive) To enter into battle.  examples

To interact contractually.

1. (transitive) To arrange to employ or use (a worker, a space, etc.).  quotations  examples

   Quotations

   • For this scene, a large number of supers are engaged, and in order to further swell the crowd, practically all the available stage hands have to ‘walk on’ dressed in various coloured dominoes, and all wearing masks.

     1905, Baroness Emmuska Orczy, chapter 2, in The Affair at the Novelty Theatre‎

2. (intransitive) To guarantee or promise (to do something).  examples

3. (transitive) To bind through legal or moral obligation (to do something, especially to marry) (usually in passive).  quotations  examples

   Quotations

   • […] Love is a ſort of Devotion too, and not only ſhould beget Reſpect, but likevviſe ingage Patience.

     , Tho[mas] d’Urfey, The Old Mode & the New, or, Country Miss with Her Furbeloe. A Comedy. […], London: […] Bernard Lintott, and sold by Samuel Clark, […], Francis Faucet […], and Lucas Stowkey […], Act I, scene i, page 1

4. (obsolete, transitive) To pledge, pawn (one's property); to put (something) at risk or on the line; to mortgage (houses, land).  quotations

   Quotations

   • Thou that doest liue in later times, must wage / Thy workes for wealth, and life for gold engage.

     1590, Edmund Spenser, “Book II, Canto VII”, in The Faerie Queene. […], London: […] [John Wolfe] for William Ponsonbie

To interact mechanically.

1. To mesh or interlock (of machinery, especially a clutch).  quotations  examples

   Quotations

   • The Liner train wagon is a simple underframe on bogies, with coned location points that engage recesses in the container bases.

     1964 April, G. Freeman Allen, “The BRB shows traders the Liner train prototypes”, in Modern Railways, page 265

2. (engineering, transitive) To come into gear with.  examples

(intransitive) To enter into (an activity), to participate (construed with in).  quotations  examples

(transitive, obsolete) To entangle.