Sept 6 (Reuters) - Texas Capital Bancshares Inc said on Tuesday it had agreed to sell its insurance premium finance unit to Truist Financial Corp for $3.4 billion, in a bid to re-focus on its core businesses and manage expenses.

The unit, BankDirect Capital Finance, will operate as a division of AFCO Credit Corporation, Truist's insurance premium finance business in the United States.

Premium financing refers to the practice of taking out loans to pay insurance premiums.

Dallas-based Texas Capital, which is the parent firm of Texas Capital Bank, said it would streamline operations and deploy resources to its core businesses.

BankDirect Capital Finance, founded in 2005, offers property and casualty as well as life insurance products. The company has 122 employees and five offices in the United States.

The deal is expected to close in the fourth quarter of this year, the company said.

(Reporting by Niket Nishant in Bengaluru; Editing by Krishna Chandra Eluri)