Does partial pressure change with altitude?
Yes or... No ! It depends...
Yes if the gases are not in a container or are in a container like a balloon which can change volume. No if the gases are in a rigid container whose volume will not change.
Partial pressure can be calculated using Dalton's Law.
Let's imagine two gases in a balloon with a total pressure of 1 atm. If gas A has a pressure of 0.4 atm, the pressure of gas B must be 0.6 atm.
Higher altitudes have lower pressures, so the balloon will expand to a larger volume with a lower internal pressure. If the balloon is brought to an altitude where the total pressure is 0.5 atm, the pressure of gas A will now be 0.2 atm and the pressure of B will be 0.3 atm.
So here is the no...
If the gases are in a sealed container which is rigid (won't change shape or volume) the partial pressures of the gases will not change because the total pressure of the gas will not change.
Hope this helps.