Irrational dread of a snake (5)
I believe the answer is:
adder
'a snake' is the definition.
(adder is a kind of snake)
'irrational dread' is the wordplay.
'irrational' indicates anagramming the letters.
'dread' with letters rearranged gives 'ADDER'.
'of' acts as a link.
(Other definitions for adder that I've seen before include "Britain's only venomous snake" , "Venomous sort" , "Type of snake" , "exhibit in the reptile house" , "He's making an extension" .)