It's a lot older than you (4)
I believe the answer is:
thee
'you' is the definition.
(historical second person pronoun)
'it's a lot older' is the wordplay.
'a lot' means to remove the last letter (I've seen 'a lot of' mean this).
'older' becomes 'hee' (I can't explain this - if you can you should believe this answer much more).
'ts' with its last letter taken away is 't'.
't'+'hee'='THEE'
'than' is the link.
Can you help me to learn more?
(Other definitions for thee that I've seen before include "'U'" , "Old objective second person singular" , "Poetically you" , "Archaic form of 'you'" , "you many years ago" .)