Republic Bank. Republic Bank is a Louisville, Kentucky-based bank that offers a variety of personal and business products, as well as convenient online and mobile banking services. Open an account online today!. bank, banking, banks, online banking, internet banking, bank account, checking , checking account, checking accounts, savings account, savings accounts, savings, ira, iras, cds, certificates of deposit, loans, online checking account, online savings account, online mortgage application, community bank, financial institution, CDs, mortgage, treasury management, money market account, money market account, money management, manage money, refi, refinance, home equity, heloc, home equity loan, line of credit, debit card, mastercard, visa, credit card, private banking, business banking, small business, commercial banking, commercial lending, business checking, business savings, debit card, moneymanager checking, mobile banking, mobile deposit.