Bank workers in Tayside and Fife will be informed today whether their branch is one of dozens planned for closure.
TSB is to cut around 300 jobs in Scotland and close 73 branches north of the border next year as part of wider cuts across the high street bank.
A “significant change in customer behaviour” has driven the decision, the bank said, with more people also adopting digital banking.
TSB operates four branches in Dundee as well as Broughty Ferry’s Brook Street.
It has four branches in Angus – in Arbroath, Carnousite, Montrose and Forfar .
The bank operates from Perth, Coupar Angus, Pitlochry, Aberfeldy, Blairgowrie and Crieff.
TSB also has sites in Rosyth, Dunfermline, Cowdenbeath, Cupar, Burntisland, Glenrothes, Buckhaven, Leven, St Andrews, Anstruther and two sites in Kirkcaldy.
The bank shut branches in Kinross and Brechin this year as part of a previous round of branch closures.
The Edinburgh-based company said the branches earmarked for closure in 2021 have been selected to ensure 94% of customers in Scotland are still within 20 minutes’ travel time of one that will remain open.
It said it will continue to invest in its 62 remaining Scottish branches over the next two years “to radically improve the customer experience”.
As part of that investment, 50 mobile advisers will be introduced in some rural communities to help existing customers and organise further support.
Robin Bulloch, TSB customer banking director, said: “These decisions are the most difficult we take, but we must always be guided by our customers – and we are clearly witnessing a substantial shift towards digital banking.
“We operate a more extensive branch network than most other banks in Scotland, including some much larger than TSB, and we need to reduce its size to reflect the changing needs of our customers and a fast-evolving operational environment.
“TSB remains committed to offering high-quality banking services in branches across Scotland.
“We are also introducing mobile advisers to ensure we look after vulnerable customers and those in rural locations.
“We are working to ensure the transition towards digital – which is being seen right across the economy – is handled sensitively and pragmatically for our colleagues and customers.”
Across the UK, the Spanish-owned bank will cut around 900 jobs and close 164 branches.
It will leave TSB with 290 branches, more than halving its store estate over the past seven years.