M-ary QAM assuming equiprobable data symbols has the carrier suppressed in both the in-phase and quadrature signals as well as the composite complex signal. Therefore a traditional PLL does not have any carrier to lock to, however additional processing can recreate a spectral tone for a PLL to lock to.
For QAM, raising the signal to the fourth power will create a strong spectral line at 4x the carrier, which an analog or digital PLL can lock to serving as a tunable bandpass filter and cleaning up the 4x recovered carrier. The recovered tone can then be divided by four to create a synchronous carrier. This approach is feasible in digital receivers operating at baseband I and Q where the “carrier” would typically be a small frequency offset (due to Doppler and offsets between transmitter and receiver clock), well below the limits of Nyquist provided by the sampling clock. In Digital IF receivers other techniques would be more practical to limit the requirements on the maximum sampling rate needed.
This is demonstrated with the example spectrums below showing a 16-QAM waveform with a frequency offset, and the spectrum of the waveform raised to the 4th power, where the strongest harmonic is at 4x the carrier frequency offset. A PLL can easily lock to the strongest tone and reject noise and side-tones that are outside of the PLL bandwidth.
Other approaches for carrier recovery use a phase detector to measure the rotation between successive samples but this ends up being a frequency discriminator (given a change in phase over a change in time is the instantaneous frequency) and therefore are used in an FLL for carrier recovery.