One's links with the old school (4)
I believe the answer is:
ties
'one's links' is the definition.
'ties' can be an answer for 'links' (tie can mean a connection or link). I'm not certain of the 'one's' bit.
'with the old school' is the wordplay.
'with' means one lot of letters go next to another.
'the' becomes 't' (the is pronounced as a 't' sound in some dialects).
'old' becomes 'ie' (I can't explain this - if you can you should believe this answer much more).
'school' becomes 'S'.
't'+'ie' is 'tie'.
'tie'+'s'='TIES'
Can you help me to learn more?
(Other definitions for ties that I've seen before include "Links" , "allegiances" , "obligations" , "Drawn games" , "Attaches, knots" .)