Straight after, call home (6)
I believe the answer is:
Here is my best explanation:
'straight' is the definition.
(associated in meaning)
'after call home' is the wordplay.
'after' says to put letters next to each other.
'call' becomes 'ho' (historical exclamation used to attract attention).
'home' becomes 'nest' (I've seen this before).
'ho' put next to 'nest' is 'HONEST'.