The odd old fella's about, it's unfashionable (5)
I believe the answer is:
dated
'unfashionable' is the definition.
(similar in meaning)
'the odd old fella's about' is the wordplay.
'odd' indicates alternate letters.
'old fella' becomes 'dad' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'about' is an insertion indicator.
The alternate letters of 'the' are 'te'.
'te' put into 'dad' is 'DATED'.
'it's' is the link.
Can you help me to learn more?
(Other definitions for dated that I've seen before include "Met socially by arrangement" , "Rusty" , "not without romantic engagements" , "Out of fashion" , "Walked out with" .)