Foreign character in Rotherhithe tavern (5)
I believe the answer is:
theta
'foreign character' is the definition.
(Greek letter)
'in rotherhithe tavern' is the wordplay.
'in' indicates the answer is hidden within the clue.
'THETA' can be found hidden inside 'rotherhithe tavern'.
(Other definitions for theta that I've seen before include "Character from overseas" , "character in Euripides" , "Greek letter used in trigonometry" , "Letter before iota" , "Homeric character" .)