Halimar Wavewatch

If another creature becomes a copy of a leveler, all of the leveler’s printed abilities — including those represented by level symbols — are copied. The current characteristics of the leveler, and the number of level counters on it, are not. The abilities, power, and toughness of the copy will be determined based on how many level counters are on the copy.

The abilities a leveler grants to itself don’t overwrite any other abilities it may have. In particular, they don’t overwrite the creature’s level up ability; it always has that.

A creature’s level is based on how many level counters it has on it, not how many times its level up ability has been activated or has resolved. If a leveler gets level counters due to some other effect (such as Clockspinning) or loses level counters for some reason (such as Vampire Hexmage), its level is changed accordingly.