One given lead in Mexico? (9)
I believe the answer is:
chihuahua
'one given lead' is the definition.
(breed of dog)
I don't understand the remainder of the clue.
Can you help me to learn more?
(Other definitions for chihuahua that I've seen before include "Dog breed from Mexico" , "Breed of tiny dog" , "Breed of small, short-haired dog" , "that's running very low?" , "Mexican state -- breed of dog" .)