Old regret backing common currency (4)
I believe the answer is:
euro
'common currency' is the definition.
(currency of the European common market)
'old regret backing' is the wordplay.
'old' becomes 'o' (common abbreviation eg in OE for Old English).
'regret' becomes 'rue' (to rue something is to regret it).
'backing' says the letters should be written in reverse.
'o'+'rue'='orue'
'orue' in reverse letter order is 'EURO'.
(Other definitions for euro that I've seen before include "EU money" , "International currency unit" , "Currency of Finland" , "Major currency" , "Foreign currency" .)