This move comes in response to a drop in cash demand spurred on by the increase of electronic transactions.
ATM operators who maintain cash points will receive up to £2.75 per cash withdrawal, while bank customers continue to withdraw their cash without paying fees themselves.
"It is vital we continue to provide free access to cash to those who need it,"
Link's move follows a row over plans for a phased reduction in interchange rates, the fee operators receive from banks.
The fee is being cut from 25p to 20p over the next three years but the move which led to accusations that "cash deserts" could be created as operators shut less lucrative machines.
There are more than 50,000 free-to-use ATMs across the UK - and the vast majority will not be eligible for the new super premiums.
Currently, around 3,500 ATMs are protected - because they are more than 1km away from the next nearest free machine or are located in particularly deprived parts of the country where access to cash is vital.
"These premiums will further safeguard ATMs in remote and less well-off areas,"
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