The translator has to use expressions in the target text (that are different from those in the source text).
I hope "that" can refer to expressions, but I feel it will refer to "the target text" if I put "that" after "the target text".
I guess I can say something like
The translator has to use expressions different from those in the source text in the target text
but I feel it sounds very awkward.
In this case, how can "that" refer to "expressions"?