Went out with note penned by father (5)
I believe the answer is:
dated
'went out with' is the definition.
('date' can be a synonym of 'go out with')
'note penned by father' is the wordplay.
'note' becomes 'te' (musical note).
'penned by' indicates putting letters inside (inserted letters are penned in).
'father' becomes 'dad' (informal term for father).
'te' placed into 'dad' is 'DATED'.
(Other definitions for dated that I've seen before include "out of the ark" , "Walked out with" , "old > saw" , "Unfashionable" , "No longer fashionable or current" .)