In this paper, we try to demonstrate a method to generate new class of exact solutions to the Einstein’s field equations (EFE) by introducing a new parameter (κ) in the Vaidya–Tikekar metric ansatz describing a static spherically symmetric relativistic star having anisotropic fluid pressure. We particularly obtained solutions in closed form in terms of trigonometric functions. Introduction of a new parameter in the metric ansatz predicts some interesting results. In our formalism, the main feature of the new class of solutions is that one can study the effects of the new parameter (κ) on different physical parameters of a compact object such as its mass, radius, surface redshift etc. Moreover, if we switch off the new parameter (κ = 0), it also gives new realistic solutions which arethe modified version of isotropic Matese–Whitman solutions in the presence of pressure anisotropy. Consequently, we present here that a plethora of well-known stellar solutions can be identified as sub-class (κ = ±1) of ourclass of solutions. We predict here the maximum mass of compact object in isotropic case and also in the presence of pressure anisotropy. The central density is found to be as high as ∼10$^{15}$ gm/cc and thus the present model is capable enough to accommodate a wider class of compact objects. We examine the physical viability of solutions for studying relativistic compact stars and it is found that all the stability conditions are satisfied.