Agent with old-fashioned hat: cold-blooded one (7)
I believe the answer is:
'cold-blooded one' is the definition.
(I've seen this in another clue)
'agent with old-fashioned hat' is the wordplay.
'agent' becomes 'rep' (short for representative).
'with' says to put letters next to each other.
'old-fashioned hat' becomes 'tile' (old-fashioned term for a hat).
(Other definitions for reptile that I've seen before include "eg Crocodile" , "Despicable sort" , "Turtle, for example" , "Snake or crocodile, say" , "Malignant creature" .)