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By using the relativistic precession model, we have studied frequencies ofquasi-periodic oscillations in the spacetime of a disformal Kerr black hole.This black hole owns an extra disformal parameter and belongs to a class ofnon-stealth solutions in quadratic degenerate higher-order scalar-tensor(DHOST) theories. Our result shows that only the periastron precessionfrequency is related to the disformal parameter, while the azimuthal frequencyand the nodal precession frequency are identical with those in the usual Kerrblack hole in general relativity. Combing with the observation data of GROJ1655-40, we fit parameters of the disformal Kerr black hole, and find that thedisformal parameter $\alpha$ is almost negative in the range of $1 \sigma$,which implies the negative disformal parameter $\alpha$ is favored by theobservation data of GRO J1655-40.

Testing gravity of a disformal Kerr black hole in quadratic degenerate higher-order scalar-tensor theories by quasi-periodic oscillations