Acknowledges obsolete currency in islands (6)
I believe the answer is:
admits
'acknowledges' is the definition.
('admit' can be a synonym of 'acknowledge')
'obsolete currency in islands' is the wordplay.
'obsolete currency' becomes 'dm' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'in' means one lot of letters goes inside another.
'islands' becomes 'aits' (I have seen 'Small islands' mean 'aits' so perhaps 'islands' could also mean 'aits').
'dm' placed within 'aits' is 'ADMITS'.
Can you help me to learn more?
(Other definitions for admits that I've seen before include "Confesses or allows to enter" , "Does not deny" , "Lets in and confesses" , "Concedes" , "Takes in" .)