Put ethane out to increase risk (2,3,4)
I believe the answer is:
up the ante
'increase risk' is the definition.
(poker)
'put ethane out' is the wordplay.
'out' indicates an anagram (out can mean wrong or inaccurate).
'put'+'ethane'='putethane'
'putethane' is an anagram of 'UP THE ANTE'.
'to' is the link.
(Other definitions for up the ante that I've seen before include "Increase what is at stake" , "Raise the stakes in poker game" , "Increase the stakes" , "increase danger?" , "increase risk" .)