What is the Chinese translation for "endure and move on"?
It's often better to provide the whole English sentence for translation. As divergent as the two language can go, a phrase-to-phrase translation is often less than pragmatic.

What I can get is "忍受悲伤, 继续前行". But as Stan said, if you move on, you usually put away your sorrows, or 抛却悲伤 instead.

There is a phrase from classical Chinese, "隐忍以行". It is an exact structural match to your phrase. However, it implies endurance for a greater cause than love.