(to), go along (with), meet the expectations (of), satisfy (obligations of courtesy)," borrowed from Spanish cumplir in this sense, from the earlier transitive senses "carry out, execute, fulfill," going back, with conjugation change, to Latin complēre "to fill" — more at complete entry 1

NOTE: The verb comply appears more likely to have been borrowed directly from Spanish rather than via Italian (pace the Oxford English Dictionary, first edition). Its use in literate discourse may have grown out of the vogue for Spanish romances that began with The mirrour of princely deedes and knighthood, a translation by Margaret Tyler of Diego Ortúñez de Calahorra's Espejo de príncipes y caballeros that was first printed in 1578. An early example of comply in the relevant sense occurs in another translation of Espejo, by "R.P." (Robert Parry or Parke), printed about 1586: "that the counsaile which you doe aske of your nobles & subiects, is more to complie with them, than anie good will you haue to be counsailed" (The third part of the first booke, of the Mirrour of knighthood). The form of the verb shows assimilation to other verbs ending in -ply, as apply, imply, reply entry 1, and supply entry 1 (which, excepting the last, are not etymologically related).