"Continuing the story" in Engpsh can be expressed as "carry on the story" or "continue the tale".

This phrase is used to indicate that the speaker or writer wants to proceed with writing or telpng a story that was previously started.

Examples:

"Can you carry on the story from where we left off?"
(中文翻译："你能从上次停下的地方继续写故事吗？")

"I would pke to continue the tale, if you don't mind."
(中文翻译："如果你不介意，我想继续写故事。")