Most important here is your noise reduction and sharpening settings. ONLY touch those while zoomed into 1:1. If you are zoomed out in Develop, your preview will be inaccurate for images with lots of noise if your develop detail settings are extreme. Only the preview in Library will be good. Does the preview in Library look like your exported images? Make sure you use a color managed app to view the export.
It is also possible that your display profile is corrupt which can have the effect of plugging up shadows in Develop and for exports looking differently. Fix this by recalibrating it. Also try if disabling GPU support in preferences->performance makes a difference for rendering in Develop. If so, your graphics card drivers are out of date or your display profile is bad.
This appears to be a high ISO image file that has insufficient LrC Luminace Noise Reduction and/or excessive Sharpening applied. As Jao suggests adjust the Detail panel controls at 1:1 100% Zoom view to reduce any visible noise.