Caught Igor going off with the dog (5)
I believe the answer is:
corgi
'the dog' is the definition.
(corgi is a kind of dog)
'caught igor going off' is the wordplay.
'caught' becomes 'c' (cricket abbreviation).
'going off' is an anagram indicator (letters go or move around).
'igor' is an anagram of 'orgi'.
'c'+'orgi'='CORGI'
'with' acts as a link.
(Other definitions for corgi that I've seen before include "Cardigan, possibly" , "pet in 9 [CARDIFF]?" , "Pre-2018 royal dog" , "Dog at Buckingham Palace" , "man's best friend" .)