Sense

1. (with genitive, often with the associated idea of a body of water), on the other side, across
2. (absolute) on the other side
3. (with verbs of motion, followed by εἰς ‎(eis)) over or across to
4. (with the article)

Examples

• καὶ παρεγένοντο εἰσ ἅλωνα Ἀτάδ, ὅ ἐστι πέραν τοῦ Ἰορδάνου, καὶ ἐκόψαντο αὐτὸν κοπετὸν μέγαν καὶ ἰσχυρὸν σφόδρα. καὶ ἐποίησε τὸ πένθοσ τῷ πατρὶ αὐτοῦ ἑπτὰ ἡμέρασ. (Septuagint, Liber Genesis 50:10)
• καὶ εἶδον οἱ κάτοικοι τῆσ γῆσ Χαναὰν τὸ πένθοσ ἐπὶ ἅλωνι Ἀτὰδ καὶ εἶπαν. πένθοσ μέγα τοῦτό ἐστι τοῖσ Αἰγυπτίοισ. διὰ τοῦτο ἐκάλεσε τὸ ὄνομα αὐτοῦ Πένθοσ Αἰγύπτου, ὅ ἐστι πέραν τοῦ Ἰορδάνου. (Septuagint, Liber Genesis 50:11)
• καὶ ἐξάραντεσ ἐξ Ὠβώθ, καὶ παρενέβαλον ἐν Ἀχαλγαὶ ἐκ τοῦ πέραν ἐν τῇ ἐρήμῳ, ἥ ἐστι κατὰ πρόσωπον Μωάβ, κατ’ ἀνατολὰσ ἡλίου. (Septuagint, Liber Numeri 21:11)
• καὶ ἐκεῖθεν ἀπάραντεσ παρενέβαλον εἰσ τὸ πέραν Ἀρνῶν ἐν τῇ ἐρήμῳ, τὸ ἐξέχον ἀπὸ τῶν ὁρίων τῶν Ἀμορραίων. ἔστι γὰρ Ἀρνῶν ὅρια Μωὰβ ἀνὰ μέσον Μωὰβ καὶ ἀνὰ μέσον τοῦ Ἀμορραίου. (Septuagint, Liber Numeri 21:13)
• Καὶ εἶπε Κύριοσ πρὸσ Μωυσῆν. ἀνάβηθι εἰσ τὸ ὄροσ τὸ ἐν τῷ πέραν τοῦ Ἰορδάνου καὶ ἰδὲ τὴν γῆν Χαναάν, ἣν ἐγὼ δίδωμι τοῖσ υἱοῖσ Ἰσραὴλ ἐν κατασχέσει. (Septuagint, Liber Numeri 27:12)

Source: Ancient Greek entries from Wiktionary