Persuaded to take an exotic drug out East (5)
I believe the answer is:
urged
'persuaded' is the definition.
(I've seen this in another clue)
'an exotic drug out east' is the wordplay.
'an exotic' indicates an anagram (an unusual form of the letters).
'out' is an insertion indicator.
'east' becomes 'e' (abbreviation).
'drug' is an anagram of 'urgd'.
'urgd' going around 'e' is 'URGED'.
'to take' is the link.
(Other definitions for urged that I've seen before include "Incited" , "Exhorted or prodded" , "Beseeched" , "Pressed" , "Strongly recommended" .)