Since we're now in Series 4, if you do not have a past series reward button visible, you have already claimed everything that you earned in Series 3.

If you didn't grind it out back then, you're out of luck now. Current series points are only applied to the current series.

As for when/if previous series rewards will become available again, that is currently unknown at this time. It was originally thought way back when the series pass was introduced that previous rewards would just move to the crystal trophy vendor but that didn't turn out to be the case. My personal theory is that the old rewards will most likely have to wait for it to be part of some future mogtome event.