Left in party to secure first big majority (9)
I believe the answer is:
landslide
'big majority' is the definition.
(I've seen this before)
'left in party to secure first' is the wordplay.
'left in party' becomes 'slide' (I can't justify this - if you can you should give a lot more credence to this answer).
'to secure' becomes 'land' (land can mean to secure or obtain).
'first' is a charade indicator (letters next to each other).
'slide' put after 'land' is 'LANDSLIDE'.
Can you help me to learn more?
(Other definitions for landslide that I've seen before include "Overwhelming election win" , "Runaway" , "Movement at grass-roots level" , "Large earth movement" , "Overwhelming election majority" .)