Not happy to put a bit of tarragon in the sauce (5)
I believe the answer is:
sorry
'not happy to put a bit' is the definition.
I can't tell whether this definition defines the answer.
'tarragon in the sauce' is the wordplay.
'tarragon' becomes 'rr' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'in the' indicates putting letters inside.
'sauce' becomes 'soy' (soy sauce).
'rr' inserted within 'soy' is 'SORRY'.
'of' acts as a link.
Can you help me to learn more?
(Other definitions for sorry that I've seen before include "Rueful" , "I beg your pardon" , "Repentant" , "Showing regret" , "Feeling penitent" .)