Travel isn't necessarily required for them to do their jobs, but neither is staying in one place.
他们的工作未必需要出差,但也不一定要固定待在一个地方。
neither 位于分句句首,表示“也不”,用于承接前面的否定分句。此时助动词或 be 动词要置于主语之前,因此正常语序 staying in one place is neither would be transformed here into neither is staying in one place。这里 is 提前,但主语 staying in one place 仍然保留,所以属于部分倒装。