Identify personal problem offering hopeful treatment (7)
I believe the answer is:
placebo
'hopeful treatment' is the definition.
(treatment which may have a placebo effect)
'identify personal problem' is the wordplay.
'identify' becomes 'place' (synonyms).
'personal problem' becomes 'bo' (informal abbreviation for body odour).
'place'+'bo'='PLACEBO'
'offering' acts as a link.
(Other definitions for placebo that I've seen before include "False medication, psychologically applied" , "Prescription to soothe" , "harmless drug" , "Spoof medicine" , "innocuous dose" .)