What roles do they play during retraction and extension of a landing gear ?
A priority valve will manage the flow in a hydraulic supply that feeds two different circuits such that if the input flow, that is normally enough to satisfy both circuits' demands, drops below a threshold, the valve will starve or cut off the low priority circuit in favour of the high priority circuit to keep it supplied. So if I have two subcircuits in a system running on the same source, and I determine that one is critical to safety, I'll put in a priority valve to make sure the critical circuit continues to get pressure if the inlet flow is not able to supply both.
Not to be confused with shuttle valves in brake systems that block off one inlet when pressure is applied at the other inlet.
Sequence valves require a mechanical condition (or electrical condition in the case of a solenoid sequence valve) to be satisfied before supplying or cutting pressure to a circuit. Like to control gear doors that need to be timed to open or close when the gear legs are at position X or Y.