Changing the harvesting time of apples from the optimum harvest window to delayed harvesting may be applied if it is impossible to harvest apples at the optimal time, but it requires changing other factors, as they influence the quality of fruits and shelf life. The aim of the study was to assess the quality of ‘Red Jonaprince’ apples during storage after delayed harvesting and 1-methylcyclopropene (1-MCP) preharvest and postharvest treatment for various storage times. Apples were studied within four groups subjected to preharvest and postharvest treatments, as follows: Group 0—no 1-MCP treatment; Group 1—1-MCP preharvest treatment; Group 2—1-MCP postharvest treatment; and Group 3—1-MCP preharvest and postharvest treatment. All apples were subjected to ultra-low oxygen (ULO) storage conducted for 3, 5 or 6 months, while the analyses were conducted directly after ULO storage (simulated shelf life—0 days) and after simulated shelf life (7 days). For firmness, in the case of 1-MCP applied only preharvest (Group 1) and only postharvest (Group 2), before shelf life, the longer ULO storage resulted in obtaining lower values of firmness (p < 0.0001). If 1-MCP was not applied postharvest (Group 0 and Group 1), and short ULO storage was applied (3 and 5 months for Group 0; 3 months for Group 1), after shelf-life lower values of firmness were observed (p < 0.0001). For soluble solids content (SSC), in the case of 1-MCP not applied preharvest (Group 0 and Group 2), before shelf life, and for 1-MCP applied postharvest (Group 2) after shelf life, the longer ULO storage resulted in obtaining lower values of SCC (p < 0.0001). For titratable acidity (TA), in the case of all the studied groups after shelf life, as well as in case of 1-MCP applied only preharvest (Group 1) also before shelf life, the longer ULO storage resulted in obtaining lower values of TA (p < 0.0001). Except for the 1-MCP applied only postharvest (Group 2), in the case of short ULO storage applied (3 and 5 months for Group 0; 5 months for Group 1; 5 months for Group 3), after shelf-life lower values of TA were observed (p < 0.0001). If delayed harvesting must be conducted, applying 1-MCP not only postharvest, but also preharvest, allows obtaining the most stable firmness and SSC, which do not decrease during storage and shelf life. Taking this into account, it may be concluded, that in the case of delayed harvesting, combining 1-MCP applied preharvest and postharvest should be recommended to keep the quality parameters stable during storage and shelf life.