clinch a/the deal = succeed in finalizing an/the agreement After months of negotiations, Sadat and Begin clinched the deal in Camp David. It's a very colloquial use, and I don't recommend it in reports.

it's an idiom " Clinch a deal " in a business relationship , if you clinch a deal , you reach agreement on a proposal or offer .

I think you will understand better if you know the meaning of clinch, and not just the phrase. Clinch: secure, grip Deal: an agreement, sale So it literally means "to secure a deal" or "to secure an agreement". This generally is used in sales or maybe business mergers.

"to clinch" is a verb to clinch a deal = to make (/conclude) a deal (/bargain)

clinch a deal= settle conclusively; come to terms regarding a business proposition