Eluding stray pet (7)
I believe the answer is:
indulge
'pet' is the definition.
(I've seen this before)
'eluding stray' is the wordplay.
'stray' indicates an anagram.
'eluding' is an anagram of 'INDULGE'.
(Other definitions for indulge that I've seen before include "Humour; spoil" , "Give free rein to" , "Favour, gratify" , "Gratify, spoil" , "Gratify (an appetite)" .)