Crossword Genius

Incidentally, see you around Thursday (2,3,3)

Ross

I believe the answer is:

by the bye

'incidentally' is the definition.
('by the bye' can be a synonym of 'incidentally')

'see you around thursday' is the wordplay.
'see you' becomes 'byebye' (I've seen this before).
'around' is an insertion indicator.
'thursday' becomes 'th' ('Th' can be a synonym of 'thursday').
'byebye' enclosing 'th' is 'BY THE BYE'.

(Other definitions for by the bye that I've seen before include "In passing" , "Parenthetically" , "Incidentally" .)

I've seen this clue in The Independent.
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