Wrong to restrict core of something remembered for all time (8)

I believe the answer is:
immortal
'remembered for all time' is the definition.
(I've seen this in another clue)
'wrong to restrict core of' is the wordplay.
'wrong' becomes 'immoral' (similar in meaning).
'to restrict' indicates putting letters inside (restrict can mean pen in or contain).
'core of' becomes 't' (I am not sure about this - if you are sure you should believe this answer much more).
'immoral' placed around 't' is 'IMMORTAL'.
'something' is the link.
I am not very happy about this link. It may belong to another bit of the clue.
Can you help me to learn more?
(Other definitions for immortal that I've seen before include "Never dying" , "Moral Tim (anag.)" , "Living forever" , "Great person" , "Living for ever" .)
