Thanks judge for a cap (3)
I believe the answer is:
taj
'cap' is the definition.
(I know that taj is a type of cap)
'thanks judge' is the wordplay.
'thanks' becomes 'ta' (UK informal version of 'thank you').
'judge' becomes 'j' (abbreviation for judge).
'ta'+'j'='TAJ'
'for a' is the link.
(Other definitions for taj that I've seen before include "Old Indian crown" , "The ... Mahal is a famous tomb in India" , "The ... Mahal is famous Indian tomb" .)