Taking nap in an old car shows the advancing years (4,6)
I believe the answer is:
anno domini
'the advancing years' is the definition.
'taking nap in an old car' is the wordplay.
'taking' means one lot of letters goes inside another.
'nap' becomes 'nod' (both can mean to sleep).
'in an old' becomes 'ano' (I can't explain this - if you can you should believe this answer much more).
'car' becomes 'mini' (Mini Cooper).
'nod' placed inside 'ano' is 'annodo'.
'annodo'+'mini'='ANNO DOMINI'
'shows' is the link.
(Other definitions for anno domini that I've seen before include "having a date, she may put it on" , "Advancing old age (informal)" , "In the year of our Lord" , "AD in full" , "later days" .)