As the conversation progressed, his eloquence grew sharper and sharper.
Literal
Talk [subject-が] advance [as-につれ] his eloquence [topic-は] increasingly sharpened.
~につれ(て) marks a proportional change: the more the talk continued, the better he spoke. 弁舌 (べんぜつ, 'eloquence, oratory') is formal vocabulary. さえる/冴える ('to be sharp, clear') here describes rhetorical brilliance. ますます ('increasingly') reinforces the escalation.