The knowledge of the origin and statistical properties of diffuse radio emission in galaxy clusters has appreciably improved thanks to the GMRT Radio Halo Survey, a project based on 610 MHz observations of clusters belonging to a statistically complete sample. However, the spectral properties of cluster diffuse sources are still poorly known and uncertain. High sensitivity and multi-resolution observations at low frequency ($le$0.3 GHz) are needed for accurate spectral studies. Here, GMRT images at 325 MHz are presented for the clusters A2744, A1300, A1758N and A781, all hosting cluster-scale diffuse emission in the form of a giant halo and/or relic. These observations are part of a new observational campaign to follow up with the GMRT at 150, 235 and 325 MHz all diffuse radio sources in the cluster sample of the GMRT Radio Halo Survey and obtain detailed information on their radio spectral properties.