Dig this kind of clue -- first place! (3-4)
I believe the answer is:
put down
'dig' is the definition.
(thesaurus)
'kind of clue first place' is the wordplay.
'kind of clue' becomes 'down' (in a crossword).
'first' means one lot of letters go next to another.
'place' becomes 'put' (synonyms).
'down' put after 'put' is 'PUT-DOWN'.
'this' acts as a link.
(Other definitions for put down that I've seen before include "crushing snub" , "Quell - crushing remark (3,4;3-4)" , "defeat" , "Write" , "Record - suppress - disparage" .)