"update further" is correct and can be used in written English.
For example, you could say: "We will update further information as it becomes available."
"The local water levels are now starting to subside and once we have clear access, we will be able to update further on a planned timetable for the clean-up operation and subsequent resumption of production and fulfilment of orders.
Fox News initially stood by its reporting, saying last week that it would "continue to track developments in the story and will update further when the situation warrants".
Earlier Wednesday, Refet Kaplan, managing director of Fox News Digital, said in an email to HuffPost: "We continue to track developments in the story and will update further when the situation warrants.
Update: Further context about Tarico's professional background was added to this article after publication.
UPDATE: Further documentation of Suleiman's role in the rendition program appears in Ron Suskind's book, "The One Percent Doctrine".
Update: Further online debate about this article has focused in particular on two points: what prompted the emergency landing and how long the plane was circling.
This story is developing and will be updated further as more information becomes available.
This article was updated further to include the comment of Elizabeth Kerr, Himes' communication director.
Today's update furthers that effort.
We will update you further as information permits.
We'll update with further information once we have this.
