It's found at the end of 13 down for a while (4)
I believe the answer is:
time
'a while' is the definition.
(thesaurus)
'it's found at the end of' is the wordplay.
'it' becomes 't' (abbreviation. e.g. in 'tis).
'found' says to put letters next to each other.
'at' becomes 'im' (I can't justify this - if you can you should believe this answer much more).
'end of' suggests the final letters.
The last letter of 'the' is 'e'.
't'+'im'+'e'='TIME'
'13 down for' acts as a link.
I am not very happy about this link. Some or all of it may be part of another bit of the clue.
Can you help me to learn more?
(Other definitions for time that I've seen before include "Spell" , "Era" , "See 15" , "The father of Truth, presumably" , "Rhythm" .)