Eluding exotic pet (7)
I believe the answer is:
indulge
'pet' is the definition.
(I've seen this before)
'eluding exotic' is the wordplay.
'exotic' is an anagram indicator (an unusual form of the letters).
'eluding' with letters rearranged gives 'INDULGE'.
(Other definitions for indulge that I've seen before include "Give free rein to" , "pet" , "Honour" , "Humour; spoil" , "Favour, gratify" .)