Going out with old Penny is a giant mistake (6)
I believe the answer is:
dating
'going out with' is the definition.
('date' can be a synonym of 'go out with')
'old penny is a giant mistake' is the wordplay.
'old penny' becomes 'd' (pre-decimal abbreviation for penny).
'giant mistake' becomes 'ting' (I am not sure about this - if you are sure you should believe this answer much more).
'd'+'a'+'ting'='DATING'
Can you help me to learn more?
(Other definitions for dating that I've seen before include "Seeing" , "Imposing time code or keeping social engagement" , "Establishing the age of" , "Taking out" , "Going out with (a person)" .)