All perfect praise be to Allah, the Lord of the worlds. I testify that there is none worthy of worship except Allah, and that Muhammad, sallallahu ʻalayhi wa sallam, is His slave and Messenger.
If you wake up before the time of the current prayer ends and you know that the leakage will continue in the remaining time, then the ruling on the person who suffers incontinence applies to you. Accordingly, you should perform ablution and pray what you wish of obligatory and voluntary prayers with that ablution until the time of the current prayer ends. You may also make up for the missed prayer and perform the current prayer with this ablution as long as you know that the time of the current prayer will end before the leakage stops.
However, if you know that you have enough time to perform ablution and pray when the leakage stops, you should wait for that time and then perform ablution and pray during it.
Allah knows best.