Whenever we have a classical theory with wavelike solutions, its quantization generally gives the corresponding quantum particles. For example, Maxwell’s theory of electromagnetism predicts the existence of electromagnetic waves. So, when this classical theory is quantized we get photons, the quanta of light.
Similarly, Einstein’s theory of gravity predicts the existence of gravitational waves. Therefore, it is expected that a consistent quantization of gravity would give gravitons, the quanta of gravity ( at least in the regime where ‘nonperturbative’ effects are negligible ).
However, if we really ‘need’ to quantize gravity or not is a different question that is still not understood very well. For example, there exist ideas like “entropic gravity” in which the Einstein’s equations can be derived from some thermodynamics considerations. If gravity is really some kind of ‘entropic force’ then it would be conceptually wrong to try to quantise it and hence there would be no gravitons.