Billy got out, with heavy heart (4)
I believe the answer is:
goat
'billy' is the definition.
(thesaurus)
'got out with heavy heart' is the wordplay.
'out with' indicates an anagram (out can mean wrong or inaccurate).
'heart' means to look at the middle letters.
The central letter of 'heavy' is 'a'.
'got' mixed up with 'a' makes 'GOAT'.
(Other definitions for goat that I've seen before include "Billy - nanny" , "fool" , "Butting nanny, perhaps?" , "Domesticated animal supplying milk, meat and wool" , "heavenly sign" .)