Happen to visit for the purpose of (4,5)
I believe the answer is:
come about
'happen' is the definition.
(synonyms)
'visit for the purpose of' is the wordplay.
'visit' becomes 'come' (come can mean to make a visit).
'for the purpose of' becomes 'about' (I can't explain this - if you can you should believe this answer much more).
'come'+'about'='COME ABOUT'
'to' acts as a link.
Can you help me to learn more?
(Other definitions for come about that I've seen before include "Happen - to change course in yacht" , "turn?" .)