Drug of the central tropics, a sort of tea (6)
I believe the answer is:
opiate
'drug' is the definition.
(opiate is a kind of drug)
'central tropics a sort of tea' is the wordplay.
'central' says to take the centre.
'a sort of' is an anagram indicator.
The central letters of 'tropics' are 'opi'.
'tea' is an anagram of 'ate'.
'opi'+'ate'='OPIATE'
'of the' is the link.
(Other definitions for opiate that I've seen before include "Narcotic drug" , "Narcotic, such as morphine" , "A sedative drug" , "A poet I become on this drug" , "A drug to induce sleep" .)