Jesus referred to “the elect” several places:
If those days had not been cut short, no one would survive, but for the sake of the elect those days will be shortened. ... For false Christs and false prophets will appear and perform great signs and miracles to deceive even the elect—if that were possible. ... And he will send his angels with a loud trumpet call, and they will gather his elect from the four winds, from one end of the heavens to the otherPeter wrote to “God’s elect,”(Matthew 24:22,24,31).
who have been chosen according to the foreknowledge of God the Father, through the sanctifying work of the Spirit, for obedience to Jesus Christ and sprinkling by his blood: Grace and peace be yours in abundancePeter also wrote to those who, through their faith in God, possess godly qualities, thus keeping them effective and productive in their knowledge of Jesus Christ(1 Peter 1:1,2).
Therefore, my brothers, be all the more eager to make your calling and election sure. For if you do these things, you will never fall, and you will receive a rich welcome into the eternal kingdom of our Lord and Savior Jesus ChristThis seems to be an indication that “the elect” includes (but may not be limited to) those who know Jesus and have been saved by His blood atonement. Their “election” will enable them to “receive a rich welcome into the eternal kingdom of our Lord and Savior Jesus Christ.”(2 Peter 1:10,11).
In addition, Paul stated that God has not rejected His people, Israel
What then? What Israel sought so earnestly it did not obtain, but the elect did. The others were hardenedThe elect of Israel will be those who flee to the wilderness/desert, following the midpoint of the 70th Week. Most of them will be protected supernaturally by God for 1,260 days or 3½ years(Romans 11:7).
I believe it also is probable that some portion of that group of elect Jews will acknowledge, accept, and embrace Jesus as Messiah and Savior during the Great Tribulation period. If so, they will be caught up in the Pre-Wrath Rapture, to take place following the opening of the Sixth Seal.
It appears, then, that “the elect” are both Gentiles and Jews who have known, now know, or will know Jesus as Lord, Savior, and Messiah. They will enter, and become integral members of, His Kingdom when He comes again—whether at the primary Rapture when He returns in the clouds, or else at the end of the 70th Week when He returns physically to earth to rule and reign.