The branch, located at 45 High Street, is set to shut its doors on June 28.
Branches in Redditch, Ross-On-Wye, Solihull and Longbridge in Birmingham are also due to shut next year.
All staff impacted by the changes will have the opportunity to move to an alternative role in TSB.
TSB’s chief customer officer Robin Bulloch said: “Closing branches is an incredibly difficult decision to take, but we have to respond to the changes in the way people bank and provide the right mix of services for all our customers now and into the future.
“These changes allow us to maintain an extensive branch presence across the country. They are accompanied by a significant investment programme to upgrade branches to better suit customer needs. And, where it takes longer to get to the nearest branch, we will introduce more ‘pop-up’ services in communities.”
In recent years, the bank has seen a significant decrease in branch use, with the average number of transactions per branch falling since January 2019 and no prospect of branch transactions returning to pre-Covid levels.
Two years ago, TSB set out its intention to reduce its branch network and invest in digital services, as part of its strategy to meet the future needs of customers, but the Covid-19 pandemic has further accelerated the shift away from branch services, with customers shopping and doing more online.
Over 90 per cent of customer transactions are now carried out digitally and video banking accounts for over 90 per cent of mortgage appointments.
The branches that will close carry out around a third fewer transactions than the TSB national average. There is also a Post Office or free to use ATM within a mile of each closing branch.