Levelling up is performed between sessions. It is assumed to take training but both the time and cost are abstracted away. Shopping also happens between sessions, anyone can buy anything for book price and get any spell casting or other services for book price and sell anything for half it’s book price. NPC casters will never leave the safety of Hacston to cast a spell on the characters but for a 10% increase in fee will cast them in the portal room immediately before the start of an adventure.
Gems are converted to cash at the lower of their true value or the estimate from an appraise check and secure banking exists to store any amount of cash and any items safely.
People also heal between session, the length of time between one adventure and the next can be as long as convenient allowing full natural healing of hit point and temporary ability damage. If a character attends consecutive adventures and has a multi-day buff it may become necessary to track time between adventures in which case this paragraph should be overruled.