After an alpha or beta decay, the new nucleus is often left with extra energy. We say it is excited. It cannot keep this energy, so its protons and neutrons rearrange and the nucleus loses the extra energy by emitting a gamma ray. This is called nuclear rearrangement.
A gamma ray is electromagnetic radiation. It has no mass and no charge, so it carries energy away without taking any protons or neutrons with it. The atomic number and the mass number of the nucleus are therefore unchanged: both stay the same. For example, a nickel nucleus with atomic number 28 and mass number 60 that has just been formed by beta decay emits gamma rays and is still a nickel nucleus with atomic number 28 and mass number 60.
This is why gamma rays are often found alongside alpha or beta particles in the radiation from a source. Gamma emission alone does not change one element into another.