Real regret after end of engagement (4)
I believe the answer is:
true
'real' is the definition.
('true' can be similar in meaning to 'real')
'regret after end of engagement' is the wordplay.
'regret' becomes 'rue' ('rue' can be a synonym of 'regret').
'after' means one lot of letters go next to another.
'end of' indicates one should take the final letters.
The last letter of 'engagement' is 't'.
'rue' after 't' is 'TRUE'.
(Other definitions for true that I've seen before include "Genuine, loyal" , "Constant" , "Veracious" , "Right; genuine" , "Exact; faithful" .)