Thanks a million for the hat! (3)
I believe the answer is:
tam
'the hat' is the definition.
(thesaurus)
'thanks a million' is the wordplay.
'thanks' becomes 'ta' (UK informal version of 'thank you').
'a million' becomes 'm' (abbreviation).
'ta'+'m'='TAM'
'for' is the link.
(Other definitions for tam that I've seen before include "'Woollen cap of Scottish origin, in short (3)'" , "Headgear" , "Turn over the mat for a cap" , "Index rating for TV watching" , "...-o'-shanter, Scottish cap" .)