I would say "to broker" is an infinitive. In the sentence, it is describing "ability." Other examples: His propensity to yell at people makes him unpopular. (Here, "to yell" describes "propensity.") I gave him a book to read. (Here, "to read" describes the purpose of the book)

"To broker" means "to negotiate". I think mobile0987's comment is important, because we have a long and conplex subject. The basic structure is "Would [X] overshadow..." so we understand the structure as, ""Would [Trump's ability to... blah blah blah.. after an armistice was signed, ] overshadow..."

Here is a link that will help you understand the meaning of 'to broker' as a verb. https://www.macmillandictionary.com/dictionary/british/broker_2

Oh, no! I'm careless to the context ... The complete sentence is : "Would Trump's ability to broker a durable and verifiable peace deal -- one that has remained elusive to numerous presidents -- to formally end the Korean War, nearly 66 years after an armistice was signed, overshadow the intensifying investigations that his administration faces" So, I got that the verb is "overshadow"