Context. In recent years, high-angular-resolution observations of the dust and gas content in circumstellar discs have revealed a variety of morphologies, naturally triggering the question of whether these substructures are driven by forming planets interacting with their environment or other mechanisms. While it remains difficult to directly image embedded planets, one of the most promising methods to distinguish disc-shaping mechanisms is to study the kinematics of the gas disc. Characterising deviations from Keplerian rotation can then be used to probe underlying perturbations such as planet-disc interactions. Creating spiral structures, the latter can also be traced in the brightness temperature. Aims. In this paper, we aim to analyse the gas brightness temperatures and kinematics of a sample of 36 transition discs observed with the Atacama Large Millimeter/submillimeter Array (ALMA) to resolve and characterise possible substructures that may be tracing embedded companions. Methods. For our analysis, we use archival Band 6 and Band 7 ALMA observations of different CO isotopologues (12CO, 13CO, and C18O) and fit different Keplerian disc models (thin and thick disc geometry) to the retrieved velocity field of each disc. Results. After the subtraction of an azimuthally averaged brightness temperature profile and Keplerian rotation model from the peak brightness temperature and velocity maps, we find significant substructures in eight sources of our sample (CQ Tau, GG Tau, HD 100453, HD 142527, HD 169142, HP Cha, TW Hya, and UX Tau A) in both the brightness temperature and velocity residuals. Other sources show tentative features, while about half of our sample does not show any substructures in the temperature and kinematics that may be indicative of planet-disc interactions. Conclusions. For the first time, we compare the substructures from our analysis with various other indicators for the presence of planets. About 20% of discs show strong features such as arcs or spirals, possibly associated with the presence of planets, while the majority of discs do not present as clear planet-driven signatures. Almost all discs that exhibit spirals in near-infrared scattered light show at least tentative features in the CO data. The present data are able to reveal only very massive bodies and a lack of features may suggest that, if there are planets at all, they are of lower mass (<1–3 MJ) or may be located closer to the star within deep cavities. Deeper and higher resolution observations and modelling efforts are needed to confirm such scenarios.