Dog collar on rector gets itchy initially (5)
I believe the answer is:
corgi
'dog' is the definition.
(corgi is a kind of dog)
'collar on rector gets itchy initially' is the wordplay.
'initially' suggests taking the first letters.
The initial letters of 'collar on rector gets itchy' is 'CORGI'.
(Other definitions for corgi that I've seen before include "pet in 9 [CARDIFF]?" , "Dog popular with British royals" , "Cardigan or Pembroke dog" , "Welsh breen of dog" , "Dog of Welsh breed, royal favourite" .)