This is a noun+noun pattern, with "symptom" a noun adjunct that modifies "distress".
"distress" can't be a verb. Grammatically a clause with a finite verb can't be used at that position in a sentence. What would the subject be? What would the object be. How would a clause fit with the rest of the sentence? There is no conjunction.
But noun+noun can form a noun phrase that can be the object of the preposition "in", and the prepostional phrase "in symptom distress" modifies the noun "reduction" and the modified noun phrase "a reduction in symptom distress" is the object of "hoping for", which forms a gerund/particple phrase "hoping for .... distress" and this phrase is a sentence modifier of the main clause "people enter therapy".