Snake having firm support (5)
I believe the answer is:
cobra
'snake' is the definition.
(I know that cobra is a type of elapid)
'firm support' is the wordplay.
'firm' becomes 'co' (abbreviation for company).
'support' becomes 'bra' (a support for the breasts).
'co'+'bra'='COBRA'
'having' acts as a link.
(Other definitions for cobra that I've seen before include "Poisoner" , "Venomous hooded snake" , "Poisonous snake" , "Reptile (found in Cabinet Office Briefing Room A?)" , "Deadly snake called King" .)