Given a 1070's relatively modest power requirements, you can get away with something less than a 550W power supply, if it is a good quality unit.
What is the make and model number of your current power supply? That information will help us determine whether it's up to the task or not.
Is that the Seasonic M12II EVO 520 SS-520GM2 520W? That is actually not a bad PSU (an older design if memory serves right) but it's a decent PSU. How old is the PSU?
Also what R9 200 series card is your current card? If it is a 280 or 290 and your (ageing?) PSU can handle it with no problem at the moment it can handle a 1070 which uses around 150W. Those two use more power.
Even if it is a R9 270 those use around 150W which is the same amount as a 1070.
If the PSU is still is good shape and not too old (and if you don't plan on overclocking the 1070) I think it would be fine. Nest issue would be number of PCIE power connectors on the PSU and how many 6/8-pin connectors the 1070 you want to get wold need. I think that PSU has two 6+2-pin connectors, so that's OK too.