Make a short call and appear to be at home (4-2)
I believe the answer is:
look-in
'make a short call' is the definition.
The definition suggests a singular noun which matches the answer.
'appear to be at home' is the wordplay.
'appear' becomes 'look' (synonyms).
'to be at home' becomes 'in' ('I'm in' can mean 'I'm at home').
'look'+'in'='LOOK-IN'
'and' acts as a link.
Can you help me to learn more?
(Other definitions for look-in that I've seen before include "Make a short visit of visual sort?" , "Watch TV (colloq.)" , "Chance of success" .)