Dog beginning to twitch and be ill (4)
I believe the answer is:
tail
'dog' is the definition.
(synonyms)
'beginning to twitch and be ill' is the wordplay.
'beginning to' indicates taking the first letters.
'and' is a charade indicator (letters next to each other).
'be ill' becomes 'ail' (synonyms).
The initial letter of 'twitch' is 't'.
't'+'ail'='TAIL'
(Other definitions for tail that I've seen before include "Elongated appendage of an animal" , "Rump" , "Elongated posterior part of an animal" , "part of coat" , "Follow closely - taper (off)" .)