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' indicates anagramming the letters.
'igor' anagrammed gives 'orgi'.
'c'+'orgi'='CORGI'
'with' is the 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" .)