Dog belonging to Alec, or Giles (5)
I believe the answer is:
corgi
'dog' is the definition.
(I know that corgi is a type of dog)
'belonging to alec or giles' is the wordplay.
'belonging to' indicates a hidden word (I've seen this in other clues).
'CORGI' can be found hidden inside 'alec or giles'.
(Other definitions for corgi that I've seen before include "Royal canine" , "found in the kennels" , "Cardigan, possibly" , "One of the Queen's dogs?" , "Royal pet" .)