The beast gets me in a state! (5)
I believe the answer is:
camel
'the beast' is the definition.
(type of animal)
'me in a state' is the wordplay.
'in' indicates putting letters inside.
'a state' becomes 'cal' (short for California).
'me' placed into 'cal' is 'CAMEL'.
'gets' is the link.
(Other definitions for camel that I've seen before include "Bearer of burdens" , "African transport" , "Saharan carrier" , "Saddle animal in desert regions" , "Humped animal" .)