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there are no Apostles living today

Duh. Here Christ shows awareness of the fact that the Apostles will all die:

Jesus did not say to him: He should not die; but, So I will have him to remain till I come, what is it to thee?
(John 21:23)

Here Christ sends his Apostles as himself:

As the Father hath sent me, I also send you.
(John 20:21)

Here Christ promises that His Church will stand forever

I will build my church, and the gates of hell shall not prevail against it.
(Matthew 16:18)

Here St. Peter promises that his office will continue after his death:

12 [...] I will begin to put you always in remembrance of these things: though indeed you know them, and are confirmed in the present truth. 13 But I think it meet as long as I am in this tabernacle, to stir you up by putting you in remembrance. 14 Being assured that the laying away of this my tabernacle is at hand, according as our Lord Jesus Christ also hath signified to me. 15 And I will endeavour, that you frequently have after my decease, whereby you may keep a memory of these things.
(2 Peter 1)

Here St. Paul sends Timothy, who is not an apostle, to teach on his behalf. Timothy has the same authority as Paul, who has the same authority as Christ.

16 Wherefore I beseech you, be ye followers of me, as I also am of Christ. 17 For this cause have I sent to you Timothy, who is my dearest son and faithful in the Lord; who will put you in mind of my ways, which are in Christ Jesus; as I teach every where in every church.
(1 Corinthians 4)

Here St. Paul sends another bishop in the same role:

speak, and exhort and rebuke with all authority
(Titus 2:15)

Here St. Paul instructs the same Timothy to send other men likewise:

the things which thou hast heard of me by many witnesses, the same commend to faithful men, who shall be fit to teach others also.
(2 Timothy 2:2)

You should try reading the Catholic Bible every once in a while.