The first question is what kind of 7x57mm you have, because there are rifles out there on actions all the way back to the 1893 Mauser. ( Don't laugh; I hunt with one.)
That is why most American ammunition is held to about 40,000 cUP, or under 45,000 PSI, chamber pressure
Rem 175-gr 2,350 fps
Rem 140-gr 2,660 fps
Federal 140-gr 2,660 fps
Federal 140-gr 2,660 fps
S&B 175-gr, 2,400 fps
S&B 139-gr 2,555 fps
PPU 139-gr 2,600 fps
Hornady makes some at lower pressure and some at modern pressure ( 52,000 psi)
162-gr SST 2,450 fps
139-gr at 2,650 fps
139-gr Superperformance at 2,800 fps
Norma and RWS have ammunition with their own bullets and Norma with some Hornady and Noslers, at modern pressures.
They will all kill your red deer. Some just have a little flatter trajectory. Some are tougher than others. Start with the least expensive you can find.