Let's consider the concept of church office. Before we do that, let's consider the concept of office. An office is a permanent position with temporary incumbents. Officeholders come and go but the office remains. There are many political examples of this, viz. kings, queens, presidents, prime ministers, senators, governors, mayors, generals.
Succession, in this sense, is to take over the same duties and responsibilities.
There's a difference between succession within that official framework, and instituting that framework in the first place. Take the founder of a company. He may create administrators who will run the company after he dies or retires. But they don't succeed him in the sense of doing the same thing he did. He was the only founder. And he may have greater authority than they did, since he started the operation from scratch. He makes the rules.
Or take the transition from monarchy to democracy. Say revolutionaries abolish the monarchy and establish a representative form of government based on elective office. Before that, you had royal succession. Now you have officeholders. Within each system, processors and successors are comparable to each other, but members of one system aren't comparable to members of another system. Kings aren't comparable to elected officials. There's a paradigm shift between the role of a founder and the custodial role of officeholders. Successive officeholders didn't create the office. Their duties and responsibilities are determined by the office, whereas the founder determines the official duties and responsibilities in the first place. As the founder, his own prerogatives may be different, and more extensive, then the offices he institutes. He isn't bound by those constraints. Rather, he functions outside the system he instituted. Within the system, it's the same kind of relationship, from one incumbent to the next. But the relationship between a founder and his initial appointees or deputies is not the same kind of thing. His constitutive role is unique, including the constitutive prerogatives.
The fact that the apostles chose elders to carry on their work doesn't amount to "apostolic succession" in the sense of transferring their teaching authority to elders. That's not a logical implication of church office. That's like saying the first president is the successor to the last king. But that's equivocal. The position of president is very different from the position of an absolute monarch.
Moreover, nothing in the concept of church office requires a continuous line of succession. If, for some reason, church office was interrupted for a century, it could restart. The concept of office can be operative whether or not you have any officeholders.
Consider a hypothetical situation in which Christianity is systematically persecuted to the point where Christians die out. There are no Christians for a century. Then the brutal regime implodes. People rediscover the Bible, become Christians, and reinitialize the system of elders and deacons. It can start up at any time or place. Indeed, that happens on the mission field. It's just a question of observing the job description in the Pastorals.
Here's what the Catholic catechism says about apostolic succession:
77 "In order that the full and living Gospel might always be preserved in the Church the apostles left bishops as their successors. They gave them their own position of teaching authority."35 Indeed, "the apostolic preaching, which is expressed in a special way in the inspired books, was to be preserved in a continuous line of succession until the end of time."36
78 This living transmission, accomplished in the Holy Spirit, is called Tradition, since it is distinct from Sacred Scripture, though closely connected to it. Through Tradition, "the Church, in her doctrine, life and worship, perpetuates and transmits to every generation all that she herself is, all that she believes."37 "The sayings of the holy Fathers are a witness to the life-giving presence of this Tradition, showing how its riches are poured out in the practice and life of the Church, in her belief and her prayer."38
79 The Father's self-communication made through his Word in the Holy Spirit, remains present and active in the Church: "God, who spoke in the past, continues to converse with the Spouse of his beloved Son. And the Holy Spirit, through whom the living voice of the Gospel rings out in the Church - and through her in the world - leads believers to the full truth, and makes the Word of Christ dwell in them in all its richness."39
Problem is, you can't infer that from what the NT says about elders. The Catholic paradigm is analogous to witchdoctor to transfers his mojo to his apprentice. There's this "power" that must be transmitted from one person to the next by direct contact, like an electrical current. If the flow of energy is stopped, it can't jump over the circuit breaker and resume on the other side. The Catholic paradigm is a pagan paradigm, based on magic. A magician conveys his magical powers to a successor. If he dies before transfing his mojo, it dies with him. He's the vessel of the mojo. Unless he touches someone, and empties his mojo into a new vessel, it ends with him.