Substructures in the hot gas atmosphere of galaxy clusters are related to their formation history and to the astrophysical processes at play in the intracluster medium (ICM). The thermal Sunyaev-Zel'dovich (tSZ) effect is directly sensitive to the line-of-sight integrated ICM pressure, and is thus particularly adapted to study ICM substructures. In this paper, we apply structure-enhancement filtering algorithms to high-resolution tSZ observations (e.g., NIKA) of distant clusters in order to search for pressure discontinuities, compressions, and secondary peaks in the ICM. The same filters are applied to toy-model images and to synthetic tSZ images extracted from RHAPSODY-G cosmological hydrodynamic simulations, in order to better interpret the extracted features. We also study the noise propagation through the filters and quantify the impact of systematic effects, such as data-processing-induced artifacts and pointsource residuals, the latter being identified as the dominant potential contaminant. In three of our six NIKA-observed clusters we identify features at high signal-to-noise ratio that show clear evidence for merger events. In MACS J0717.5+ 3745 (z = 0 : 55), three strong pressure gradients are observed on the east, southeast, and west sectors, and two main peaks in the pressure distribution are identified. We observe a lack of tSZ compact structure in the cool-core cluster PSZ1 G045.85+57.71 (z = 0 : 61), and a tSZ gradient ridge dominates in the southeast. In the highest redshift cluster, CL J1226.9+3332 (z = 0 : 89), we detect a ridge pressure gradient of similar to 45 arcsec (360 kpc) in length associated with a secondary pressure peak in the west region. Our results show that current tSZ facilities have now reached the angular resolution and sensitivity to allow an exploration of the details of pressure substructures in clusters, even at high redshift. This opens the possibility to quantify the impact of the dynamical state on the relation between the tSZ signal and the mass of clusters, which is important when using tSZ clusters to test cosmological models. This work also marks the first NIKA cluster sample data release.