All right to go round home making beastly noise? (4)
I believe the answer is:
oink
'beastly noise?' is the definition.
(noise made by a pig)
'all right to go round home' is the wordplay.
'all right' becomes 'ok' (synonyms).
'to go round' is an insertion indicator.
'home' becomes 'in' ('he's home' can mean 'he's in').
'ok' placed around 'in' is 'OINK'.
'making' is the link.
(Other definitions for oink that I've seen before include "Beastly sound" , "Pig's noise" , "What you get from pen" , "Animal sound" , "Cartoon sound of pig" .)