The more common term is ‘manages’, though

κινεί τραπεζικούς λογαριασμούς = manages (or operates) bank accounts

ανοίγει και κινεί τραπεζικούς λογαριασμούς = opens and manages (or operates) bank accounts

When someone ‘κινεί’ a bank account, he credits the account with money, makes withdrawals and payments, arranges standing orders and loans, etc., and generally ‘manages’ or ‘operates’ the bank account.

See:

https://www.google.com/search?ei=JKvyX8DXMayBi-gPsYCL2A0&q="...

and

https://www.google.com/search?ei=JKvyX8DXMayBi-gPsYCL2A0&q="...

and

https://www.moneyadviceservice.org.uk/en/articles/running-yo...

https://www.investopedia.com/terms/c/cash-management.asp

or

https://www.google.com/search?biw=1243&bih=560&ei=AbPyX6a5F4...

and

https://www.google.com/search?biw=1243&bih=560&ei=yLPyX_jSJZ...


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Note added at 15 hrs (2021-01-04 07:03:12 GMT)
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Another alternative of ‘κινεί τραπεζικούς λογαριασμούς’ is ‘handles bank accounts’, see:

https://www.google.co.uk/search?ei=c7vyX9ijE4TckgWIoae4Ag&q=...

and

Opens and handles bank accounts for Cheney Ranch. Gets bids for HOA board on any work or repair projects that are needed. Hires Board's selection - then
http://www.cheneyranchhoa.com/management_co.html

but. as I have said above, the most commonly used term is, ‘manages bank accounts’.


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Note added at 1 day 4 mins (2021-01-04 15:46:56 GMT)
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Another word that is commonly used instead of managing a bank account, operating a bank account or handling a bank account is running a bank account. See:

https://www.moneyadviceservice.org.uk/en/categories/running-...

If you were to use this term, ‘κινεί τραπεζικούς λογαριασμούς’ would be ‘run bank accounts’.


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Note added at 1 day 6 mins (2021-01-04 15:48:50 GMT)
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Sorry that should have been, 'If you were to use this term, ‘κινεί τραπεζικούς λογαριασμούς’ would be ‘runs bank accounts’.

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Note added at 1 day 24 mins (2021-01-04 16:06:44 GMT)
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In your text, you could also translate ‘ανοίγει και κινεί τραπεζικούς λογαριασμούς κάθε μορφής’ as ‘opening and running bank accounts of every kind’. See:

https://www.google.com/search?ei=gjnzX6XmLs23kwXdrZmYAg&q="o...


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Note added at 1 day 15 hrs (2021-01-05 07:15:02 GMT)
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The reason why I did not include ‘runs bank accounts’ in my original answer is simply because I did not find many Internet confirmations for it, especially when referring to the duties of a manager or executive of a company or business. However, ‘run bank accounts’ and ‘running bank accounts’ are both very common expressions as you will see if you Google them in inverted commas.