Are there today?

Nope, they are all dead.

the bible itself defines
Apostle in the bible when Matthais was selected to take Judas's place:
Acts 1:21 "Therefore, of these men who have accompanied us all the time that the Lord Jesus went in and out among us, 22 beginning from the baptism of John to that day when He was taken up from us, one of these must become a witness with us of His resurrection."
23 And they proposed two: Joseph called Barsabas, who was surnamed Justus, and Matthias. 24 And they prayed and said, "You, O Lord, who know the hearts of all, show which of these two You have chosen 25 to take part in this ministry and apostleship...

 

The apostles had to have seen Christ and have been eye witnesses of what they testified (John 15:27, Acts 1:21-22, 1 Cor. 9:1, 1 John 1:1, Gal. 1:11-12, Acts 10:39-43, 2 Peter 1:16-19). God bore witness to the inspiration of the words revealed to and recorded by the apostles and prophets by signs, wonders, and miracles (heb. 2:3-4, 2 Cor. 12:12). The church is built on the foundation of the apostles and prophets (Eph. 2:20).

How could the foundation be complete if more apostles would be necessary today?

 

IMO there may not be apostles as the 12 and Paul any more, but there may be:

1) apostles as messenger's of the Church as was Titus ( I think). The term may be used in a lesser sense possibly, but not probably IMO, even of a woman as in Rom 16. There would be no occasion for apostles in the higher sense as the apostolic tradition is given already, and THAT was the function of the apostle.

2) prophets. If you will look at the content of most prophecy in the NT by such as Agabus or Philip's daughters , you will see that it concerns not eternal verities, but personal and/or temporal issues. I see no NT reason why this form of prophecy could not continue. BUT I know of no true prophet in this manner and would be highly suspicious of one who says he/she is a prophet. I've had experiences with such and find them unconvincing! If you will look at Thessalonians and 1 Cor, you will see that the church's understanding of the apostolic tradition (ie, the NT) was the authority over the virtues of a prophetic utterance. In other words, it is more vital to understand the written Word than it is to be a prophet!