On the radio, visitor conjectured (7)
I believe the answer is:
guessed
'conjectured' is the definition.
(I've seen this before)
'on the radio visitor' is the wordplay.
'on the radio' indicates a 'sounds like' (homophone) clue.
'visitor' becomes 'guest' (guest is a kind of visitor).
'guest' is a homophone of 'GUESSED'.
(Other definitions for guessed that I've seen before include "perhaps got in one" , "Thought" , "Reckoned, judged" , "Conjectured" , "Assumed" .)