Bank consolidation in the city has picked up in recent months despite erratic oil prices and flooding tied to Hurricane Harvey.
Triumph Bancorp has developed technology to help freight brokers make faster payments to truckers, charging a fee for the service.
The company agreed to buy Bank of River Oaks for $85 million in cash.
The private equity firms plan to sell a total of 3 million shares in the Houston company in coming weeks.
The Texas company will gain four branches and $160 million in loans after the acquisition closes.
The Dallas company has agreed to sell its health care lending group to an undisclosed buyer.
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The company has registered shares that three private equity firms have held since early 2010.
The purchase will significantly increase Hancock's assets under management and administration.
The company will pay $186 million for First Bank Lubbock in a deal that also includes mortgage unit PrimeWest Mortgage.