The olive tree is an iconic tree in the Mediterranean region, traditionally cultivated under rainfed conditions; however, olive cultivars are also found outside the Mediterranean region and are widely used for oil and olive production. However, with the increasing aridity and global changes, olive agroecosystems are facing sustainability challenges. This study aims to evaluate the effect of two deficit irrigation strategies on the agronomic and productive parameters of the Menara, olive cultivar as a tool for operational irrigation water management. For this purpose, an experiment was conducted on an olive orchard for two consecutive years (2021 and 2022), comparing four regulated deficit irrigation (RDI) treatments and two sustained deficit irrigation (SDI) treatments, with fully irrigated trees. The results showed that moderate and controlled water stress under RDI did not significantly affect the yield of the Menara olive cultivar. In addition, by reducing plant water requirement by 20% during sensitive periods and by 40% during normal periods, under RDI, it is possible to save between 25% and 30% of irrigation water and to increase water productivity by 5%–20% with a slight decrease in fruit yield ranging between 10% and 15%. However, the trees subjected to the sustained deficit irrigation strategy exhibited a reduced capacity for shoot growth compared to those under RDI and fully irrigated conditions. Our findings showed that water deprivation during sensitive periods reduced phenological traits and slowed down shoot growth. Furthermore, the water status of the trees was reflected in fruit volume, as a decrease in water supply resulted in a corresponding reduction in fruit volume. Although the study provides important insights into water management strategies for olive cultivation, the short observation period does not allow for long-term plant adaptation evaluation and productivity beyond 2 years. Therefore, it is recommended that future studies extend the observation period to better understand plant adaptation to irrigation regimes.