Adobe After Effects CC - stabilize lighting
I'll assume the camera op was fooling with the exposure?

You'll need to key-frame color correction or AE's Auto Color function may work for you:
https://helpx.adobe.com/after-effects/using/color-correction-effects.html

If you go the CC route it may help to watch the YC waveform rather than the image itself.

The Color Stabilizer effect may also work for you. Here's lybda "starter" explination for it youtube tutorial.