Probably from klao (through the idea of using bits of wood, etc., for the purpose; a die (for drawing chances); by implication, a portion (as if so secured); by extension, an acquisition (especially a patrimony, figuratively) -- heritage, inheritance, lot, part.
see GREEK klao
1. an object used in casting or drawing lots, which was either a pebble, or a potsherd, or a bit of wood (hence, κλῆρος is to be derived from κλάω (cf. Ellicott on Colossians 1:12)): Acts 1:26 (see below); βάλλοντες κλῆρον, Matthew 27:35; Mark 15:24; Luke 23:34; John 19:24 (Psalm 21:19 2. what is obtained by lot, allotted portion: λαγχάνειν and λαμβάνειν τόν κλῆρον τῆς διακονίας, a prrtion in the ministry common to the apostles, Acts 1:17, 25 R G; ἐστι μοι κλῆρος ἐν τίνι, dative of the thing, Acts 8:21; like κληρονομία (which see) it is used of the part which one will have in eternal salvation, λαμβάνειν ... τόν κλῆρον ἐν τοῖς ἡγιασμένοις, among the sanctified, Acts 26:18 (Wis. 5:5); of eternal salvation itself, κλῆρος τῶν ἁγίων, i. e. the eternal salvation which God has assigned to the saints, Colossians 1:12 (where cf. Lightfoot). of persons, οἱ κλῆροι, those whose care and oversight has been assigned to one (allotted charge), used of Christian churches, the administration of which falls to the lot of the presbyters: 1 Peter 5:3, cf. Acts 17:4; (for patristic usage see Sophocles Lexicon, under the word; cf. Lightfoot on Philippians, p. 246f).