Regret backing old currency (4)
I believe the answer is:
euro
'currency' is the definition.
(I've seen this before)
'regret backing old' is the wordplay.
'regret' becomes 'rue' ('rue' can be a synonym of 'regret').
'backing' says the letters should be written in reverse.
'old' becomes 'o' (common abbreviation eg in OE for Old English).
'rue' back-to-front is 'eur'.
'eur'+'o'='EURO'
(Other definitions for euro that I've seen before include "Basic monetary unit for 19 countries" , "The "single currency"" , "The new international money unit" , "Spanish currency unit" , "European currency" .)