Cardiac magnetic resonance imaging (CMR) has been widely used in clinical practice for the medical diagnosis of cardiac diseases. However, the long acquisition time hinders its development in real-time applications. Here, we propose a novel self-consistency guided multi-prior learning framework named $k$-$t$ CLAIR to exploit spatiotemporal correlations from highly undersampled data for accelerated dynamic parallel MRI reconstruction. The $k$-$t$ CLAIR progressively reconstructs faithful images by leveraging multiple complementary priors learned in the $x$-$t$, $x$-$f$, and $k$-$t$ domains in an iterative fashion, as dynamic MRI exhibits high spatiotemporal redundancy. Additionally, $k$-$t$ CLAIR incorporates calibration information for prior learning, resulting in a more consistent reconstruction. Experimental results on cardiac cine and T1W/T2W images demonstrate that $k$-$t$ CLAIR achieves high-quality dynamic MR reconstruction in terms of both quantitative and qualitative performance.

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