Jeremy peripherally traps wild cat, heading off danger (8)
I believe the answer is:
jeopardy
'danger' is the definition.
(I know that jeopardy is a type of danger)
'jeremy peripherally traps wild cat heading off' is the wordplay.
'jeremy peripherally' becomes 'jy' (I can't justify this - if you can you should give a lot more credence to this answer).
'traps' means one lot of letters goes inside another.
'wild cat' becomes 'leopard' (I've seen this before).
'heading off' means to remove the first letter.
'leopard' with its first letter taken away is 'eopard'.
'jy' enclosing 'eopard' is 'JEOPARDY'.
Can you help me to learn more?
(Other definitions for jeopardy that I've seen before include "Danger of injury, loss, death, etc" , "See 15" , "Danger of harm" , "Hazard, risk" , "Personal danger" .)