Chara can only interact via possession. If their host body is destroyed, they lose the fight via incapacitation. So, their non-corporality shouldn't really effect Grand Priest's ability to defeat them. Also, he has non-physical interaction. Their soul manipulation is interesting, but Angels can only die via EE. I don't think Chara can put GP down via Soul Manipulation.
Their main advantages are Time Manipulation and Reality Warping but, to memory, their Reality Warping isn't advanced. It's their Time Manipulation that proves troublesome for most but, the Grand Priest is immune to time hax on a multiversal-scale so...I question how effective Chara's rewinding would be. It's plausible that GP would remember resets.
There is the issue that the Grand Priest is superior to any Undertale character skill-wise. It's likely that Chara would find GP to be far more difficult to defeat than Sans. If the Grand Priest can remember resets or senses Chara's evil (which he should, it's on his profile) he can erase Chara from all of space and time. It's even stated by Beerus, that his Hakai should erase Zamasu across all timelines and the Grand Priest's EE is superior to a GoDs, due to only him and Zeno being capable of erasing Angels. If EE doesn't work, the GP has access to sealing to incap Chara.
I'm not recognising a win con for Chara. If they want to defeat someone as skilled, experienced and diverse as the Grand Priest they will need him to not remember any resets, if he remembers resets they have zero win conditions. If he doesn't remember resets, it should take Chara far more resets to adapt to, and defeat, GP than it did for them to kill Sans.
We know Sans can interpret Chara's resets, but the reasoning is unknown. If it's due to Sans' knowledge of the timelines and sharp mind, then I can picture the GP picking up on Chara's time hax, considering Time Skip, Time Stop and Time Rewinding all exist in Dragon Ball's multiverse.
Ultimately, all it takes is the GP using sealing or EE on Chara in one reset, and they lose. I'm voting for the Grand Priest, if this isn't a curbstomp.