Barked shrilly or deeply when disturbed (6)
I believe the answer is:
yelped
'barked shrilly' is the definition.
'yelped' can be an answer for 'barked' (yelping is a kind of barking). I am unsure of the 'shrilly' bit.
'deeply when disturbed' is the wordplay.
'when disturbed' indicates an anagram.
'deeply' with letters rearranged gives 'YELPED'.
'or' is the link.
Can you help me to learn more?
(Other definitions for yelped that I've seen before include "Barked" , "Uttered sharp barks" , "Cried out sharply" , "(Dog) cried in pain" , "Uttered short cry like a dog" .)