Parent penning note — that’s unfashionable (5)
I believe the answer is:
dated
'unfashionable' is the definition.
(similar in meaning)
'parent penning note' is the wordplay.
'parent' becomes 'dad' (dad can informally mean father).
'penning' means one lot of letters goes inside another.
'note' becomes 'te' (musical note as in do re mi fa so la ti).
'dad' going around 'te' is 'DATED'.
'that's' is the link.
(Other definitions for dated that I've seen before include "Unfashionably old" , "square" , "old > saw" , "Met socially by arrangement" , "Rusty" .)