The most common and most likely answer to this crossword clue is the 3 plus 4 letter word PET HATE
P
E
T
H
A
T
E
More clues leading to the result PET HATE
- Despised something which blocks leak
- Type that exasperates, somewhat
- Disillusioned vets might admit to this particular dislike
- Despised thing which plugs leak
- It’s a bugbear training with half of team around Derby perhaps
- Bête noire, fear of dogs perhaps
- Bugbear has darling husband worried
- The rogue interrupting head is a source of annoyance
Buddy explains!

The straight part
We know that "source of annoyance" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case source of annoyance = pet hate.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.