Do angler quest's start over when he dies?
Solution 1:
The Angler quests progress by a counter attached to your player data, not based on the actual Angler person. I have jumped worlds and completed quests in multiple worlds on the same character to advance my quest queue.
From the wiki:The Angler - Notes...(second to last note)
The Quest completed count is character specific, meaning you are able to accrue the number of quests required for an item given as a reward, from completing them on multiple worlds.
So if the Angler dies, your progress is still valid and will continue when the next Angler shows up.