Apology for being sad (5)
I believe the answer is:
sorry
I believe this clue is a double definition.
'apology' is the first definition.
(I have seen 'Common apology ' mean 'sorry' so perhaps 'apology' could also mean 'sorry')
'being sad' is the second definition.
('sorry' can be similar in meaning to 'sad')
'for' acts as a link.
(Other definitions for sorry that I've seen before include "Regretful, apologetic" , "My apologies!" , "I beg your pardon" , "Common apology" , "Rueful" .)