Nikon D7500 has a Nikon F lens mount and currently there are 280 native lenses available for this mount.
Nikon D7500 doesn't have a sensor based image stabilization system but 88 of these lenses already comes with optical image stabilization.
Since Nikon D7500 has a APS-C sensor, it has a focal length multiplier of 1.5x so you have to multiply lenses original focal length with this multiplier to find the Full Frame equivalent focal length of the lens when mounted on D7500.
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Nikon D7500 Lenses with Image Stabilization
Nikon D7500 Lenses with Weather Sealings