Much of the 2nd Punic War after Cannae involved Rome engaging in Fabian tactics against Hannibal and then fighting Carthage anywhere where Hannibal wasn't. After Cannae, Rome determined that they were unable to defeat Hannibal in direct battle and return to the tactics proposed by Fabius Maximus before the disaster at Cannae. Roman armies would harras and shadow Hannibals army without ever directly engaging for the rest of Hannibals time in Italy.

While this was going on, several Italian and Greek city states changed allegiance to Hannibal, not willing to stick with Rome after several crushing defeats. This had initially been Hannibal's plan, to use the Italian and Greek cities to check Roman power. Hannibal was not confident in his ability to besiege Rome and saw the changing of these cities allegiance to be a more reliable plan against Roman power.

While these city states provided Hannibal with ports, supplies, and reinforcements, they also acted as a Hannibal's downfall. Since this cities were now hostile to Rome, they required protection. Roman armies would besiege now hostile cities and force Hannibal to come to the cities aid. This was particularly problematic for Capua, whose close proximity to Rome rendered vulnerable to Roman attacks. Hannibal would even attempt to march on Rome in an attempt to relieve Capua.

Outside of Italy, Rome was waging a war in Spain against Hasdrubal Barca at the Carthage forces. Armies lead by Publius Cornelius Scipio (the father of Scipio Africanus) and his brother Gnaeus Scipio Calvus were waging successful campaigns across the Ebro river against Hasdrubal. After the defeat of Hasdrubal at the battle of Dertossa 215bc, Carthage deployed another general, known as Hasdrubal Gisco. With both the Hasdrubal's and the help of Mago Barca, the 3 generals killed both Scipio brothers in 212 bc, temporarily removing the Roman menace in Iberia.

In 211bc, Scipio Africanus (although he wasn't called that until after Zama), was elected proconsul in Spain to continue the war. Scipio's election was curious as he was only 25 at the time, normally considered too young for a political position. One potential reason is name recognition, as the Scipio name carries weight with the Celtiberian tribes. Regardless, Scipio Africanus took control of Spain in 211bc and captured Carthago Nova (new Carthage), Carthage's Spanish Capital. This completely surprised the Carthaginian generals, who reasoned it was safely protected behind its walls and left in undefended. Scipio would continue to fight in Spain until 206 bc, effectively removing Carthaginian presence in Iberia, forcing Hasdrubal to flee and attempt to join his brother and cut of Hannibal's supply of silver.

Hasdrubal attempted to join with Hannibal, but was defeated by Claudis Nero at the battle of Metaurus in 207bc. This effectively forced Hannibal into the Southern part of Italy, and eliminated Carthaginian power in Northern Italy.

There are not too many other notable events in the 13 years Hannibal is stuck in Italy. One that does stand out is the Siege of Siracusa,  2 year siege from 214-212 bc undertaken by Roman General Marcellus. This siege is notable due to Archimedes, a Greek Polymath who invented unique ways of defending Siracusa. Archimedes is supposed to have used mirror to focus sunlight to burn roman ships. Eventually Siracusa falls, leaving Hannibal without another valuable port and less control of southern Italy.

The last event I will detail is the deaths of Marcellus and his co-counsel Crispinus, who were ambushed by a large force of Numidian horsemen in 208bc. Losing both Consuls was hannibal's last victory against Rome. Hannibal even attempted to take Marcellus signet ring to try and forge some documents before news of the Consuls death spread. This proved ultimately ineffective as Rome was made aware of the deaths in time and view any signet of Marcellus as suspicious.

That pretty much covers most events between Cannae and Zama. If I missed something out I apologize and if my writing sucks, I can only blame writing on a phone.