From Dragon Mania Legends (DML) Wiki
Arena Energy is the energy used in the Dragon League each time a battle is fought. Arena Energy automatically regenerates at a rate of 1 every 1 hour and 30 minutes, up to the maximum base amount. It can also be recovered through Arena Gems (at the cost of 1 Arena Gem per energy), through Gems (at the cost of 25 Gems per energy), or through leveling up. Both methods fully replenish the energy and there is no option of choosing the amount of energy desired for replenishing when using Gems or Arena Gems. The only way to replenish the energy in smaller amounts is to use small amounts at a time and then a Trainer can replenish the amount remaining to maximum. The Arena Energy can be refilled three different ways: by pressing the button in the right-hand side of the screen and then the Use button under the Arena Gem(s), by pressing the + button in the main screen of the Dragon League, and by trying to engage a battle without any energy left (which will bring up the refill screen from where the energy can be refilled either with Arena Gems or Gems).
The base amount of energy is four. There is no way to increase the maximum base amount of Arena Energy other than by purchasing VIP Status. VIP levels 1-9 receive two energy units, VIP levels 10-18 receive three energy units, and VIP levels 19-20 receive four energy units (thus the Trainer can have a maximum of eight energy units). Fighting in the Dragon League requires 1 energy for a regular battle and two energy for a focused attack. A focused attack temporarily enhances all of the Trainer's Dragons' current Attack by 50% for that battle.
See Battle Energy for more information