"in fear that" is correct and usable in written English.
It is used to introduce a clause that expresses a fear of something. For example: "I called off the summit in fear that the negotiations would fail."
Either way, I was so gripped in fear that my mind simply stopped working.
Sarju says he lives in fear that his hut will be torched by a resentful neighbour.
But we lived in fear that someone would come back for us.
You know, we still live in fear that our family is going to be torn apart".
He lives in fear that the Taliban will come to reclaim the bodies of their bombers.
"I lived in fear that when I came home my lock would be changed," he said.
"One of us is living in fear; we're still in fear that we'll be separated".
Many live in fear that without pain, their children won't learn how to avoid hurting themselves.
Manilans live in fear that one day "the Big One" will devastate their city.
I have family and friends crying tonight in fear that Donald Trump will deport them".
"They live in fear that they don't know what is going on".
