There are not only several gaps, but there are a couple of places where there are overlaps and there were two or three popes at the same time. But that’s not really what’s being talked about when the topic is apostolic succession.
I’m going to annoy a bunch of my orthodox Catholic brothers and sisters here, but (a) Jesus didn’t ordain any priests, (b) he didn’t ordain any bishops, (c) he didn’t ordain anybody that we know of. The apostles were venerated by the early church because they were Jesus’ “inner circle” - they heard him the most and knew him the best. They passed on what they saw and heard and experienced and others came to believe what they believed. And then more leaders were needed, and each new house church raised up their own leader so that the apostles get another church started. They called these leaders “episcopos” and we translate that “bishop”, but it sure didn’t mean what it means today!
Ordination (the laying on of hands, taking vows and anointing) wasn’t a part of becoming a bishop right away - that took at least 100 years after Jesus’ resurrection, and we really don’t know a whole lot about how it was done or what it entailed, and it’s very doubtful that even then apostolic succession was a true laying on of hands by one of the apostles - it’s really doubtful that it was or could have been regulated like that. What was important that the gospel that was preached was the gospel of the senior episcopos, and that it could be traced back to the oral tradition of the “new” written versions.
And don’t even get me started on the whole pope idea! Once Constantine made Christianity the state religion, the Church and the Empire started looking and acting so much alike that the Church lost most of its identity and the episcopos started looking more like a Roman pro-consel than a shepherd and acted more like a feudal lord than our Lord. And boy oh boy, the episcopos of Rome began to look and act just like Caesar, only Caesar wasn’t a god anymore and the episcopos of Rome got his own laws, courts, armies, palaces, throne, crown and courtesans and began being known as “Vicar of Christ”.
When Jesus comes back again, there are going to be some folks who are going to have a lot of trouble explaining what happened, I think…
May the peace that Jesus has given me be yours.