A new extended exponential lifetime model called Harris extended-exponential (HEE) distribution for data modelling with increasing and decreasing hazard rate shapes has been considered. In the reliability context, researchers prefer to use censoring plans to collect data in order to achieve a compromise between total test time and/or test sample size. So, this study considers both maximum likelihood and Bayesian estimates of the Harris extended-exponential distribution parameters and some of its reliability indices using a progressive Type-II censoring strategy. Under the premise of independent gamma priors, the Bayesian estimation is created using the squared-error and general entropy loss functions. Due to the challenging form of the joint posterior distribution, to evaluate the Bayes estimates, samples from the full conditional distributions are generated using Markov Chain Monte Carlo techniques. For each unknown parameter, the highest posterior density credible intervals and asymptotic confidence intervals are also determined. Through a simulated study, the usefulness of the various suggested strategies is assessed. The optimal progressive censoring plans are also shown, and various optimality criteria are investigated. Two actual data sets, taken from engineering and veterinary medicine areas, are analyzed to show how the offered point and interval estimators can be used in practice and to verify that the proposed model furnishes a good fit than other lifetime models namely: alpha power exponential, generalized-exponential, Nadarajah-Haghighi, Weibull, Lomax, gamma and exponential distributions. Numerical evaluations revealed that in the presence of progressively Type-II censored data, the Bayes estimation method against the squared-error (symmetric) loss is advised for getting the point and interval estimates of the HEE distribution.