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β-decay is one of the key factors for understanding the r-process and evolution of massive stars. The Gamow–Teller (GT) transitions drive the β-decay process. We employ the proton–neutron quasiparticle random phase approximation (pn-QRPA) model to calculate terrestrial and stellar β-decay rates for 50 top-ranked nuclei possessing astrophysical significance according to a recent survey. The model parameters of the pn-QRPA model affect the predicted results of β-decay. The current study investigates the effect of nucleon–nucleon pairing gaps on charge-changing transitions and the associated β decay rates. Three different values of pairing gaps, namely TF, 3TF, and 5TF, were used in our investigation. It was concluded that both GT strength distributions and half-lives are sensitive to pairing gap values. The 3TF pairing gap scheme, in our chosen nuclear model, resulted in the best prediction with around 80% of the calculated half-lives within a factor 10 of the measured ones. The 3TF pairing scheme also led to the calculation of the biggest β-decay rates in stellar matter.