An extension of the current ZLindley distribution, the new one-parameter Square ZLindley distribution (SZLD) is presented in this paper. It is possible to utilise the suggested model with both left-symmetric and left-skewed data sets. The shape of the SZLD will be discussed. Additionally included are quantile functions, moment generation functions, mean lifespan functions, Rényi entropy, order statistics, and survival and hazard functions. To effectively convey the usefulness of the suggested distribution, statistical features like moments, modes, quantile functions, and moment generator functions are produced. Using the maximum likelihood estimation method, parameters were computed. A comprehensive simulation analysis is conducted to assess these suggested estimators' performance using MLE for various parameter values two real-world datasets are used to illustrate the applicability and flexibility of the newly suggested distribution. Additional statistical inferences on the SZLD are supplied by data fitting, simulation studies, and graphing, utilising R and Maple tools.