I guess it once said "Sheffield & Hallamshire Savings Bank"
Not enough space for 'and Hallamshire' but I agree about the first and last parts.
There's definitely something between "Sheffield" and "Savings" so could it be "Sheffield Trustee Savings Bank"?
Yep, that's what I thought it was.
I guess you have Googled it, but there certainly was one.....http://discovery.nationalarchives.gov.uk/details/c/F168574