I am currently in 14th place in the amateur tier for the June Kiawah 18-Hole Open.
I have sinced been updated to the pro tier.
If I play the tournament again, will it place me in the standings for pro and remove my entry for amateur?
No.
So you are saying I could technically place twice in the same tournament, under different tiers.
No. Once you enter a tournament under a particular tier, every score you record in that tournament afterward will remain in that tier, regardless of whether or not you've moved up in the interim