Can another adult tooth grow in place of an old one?

Possibly: We only have one set of permanent or secondary teeth. Some erupt under the baby teeth pushing them out. The permanent molars erupt behind the baby teeth(6 yo molar, 12 yo molar and wisdom tooth). Some are missing teeth; some get extra teeth. However, sometimes one of the permanent teeth erupt into the space of a missing tooth. Most often with a wisdom tooth filling in for lost 12 yo molar.

Not sharks: Sharks have teeth that keep replacing ones that fall out. We don´t. You only have one set of permanent teeth, normally 32 unless some don't develop. There is something called supernumerary teeth which are "extra" teeth that develop, most often between two upper front teeth. Also extra wisdom teeth sometimes. Preserve your own teeth and don't expect to get new ones like sharks.

Secondary teeth: We are genetically predisposed to form two sets of teeth, the primary (baby) teeth, and the secondary (adult) teeth. There's no third set forming to replace lost adult teeth. For that, you'll need to see a dentist.

Supernumerary tooth: Supernumerary teeth are the extra teeth that one can have in the mouth. They can be found at any location in the oral cavity. This condition is referred to as hyperdontia. The specific cause of the development of the extra teeth has not yet been established. But there are a number of theories that have been put across to explain their presence.

No: A baby tooth falls out and then the new adult tooth comes in. The "second row of permanent teeth" thing is just a myth.

No: Ws have baby teeth that are replaced by the permanent teeth. There are not extra permanent teeth except for a very rare supernumerary tooth that forms in a very few people.