Twin island in the Thames (4)
I believe the answer is:
isis
'the thames' is the definition.
(term for the River Thames in Oxford)
'twin island' is the wordplay.
'twin' shows that letters should be duplicated.
'island' becomes 'is' (abbreviation).
'is' doubled is 'ISIS'.
'in' acts as a link.
(Other definitions for isis that I've seen before include "where one might take a punt" , "Old Egyptian fertility goddess" , "Egypt. goddess" , "Egyptian deity" , "Egyptian goddess and jihadist group" .)