Ignoring the odds, cynic leads senior - one who surrenders (7)
I believe the answer is:
yielder
'one who surrenders' is the definition.
(I've seen this before)
'ignoring the odds cynic leads senior' is the wordplay.
'ignoring the odds' means one should take alternating letters (letters in odd-numbered positions are removed).
'leads' says to put letters next to each other (some letters go in front of others).
'senior' becomes 'elder' (similar in meaning).
The alternate letters of 'cynic' are 'yi'.
'yi'+'elder'='YIELDER'
(Other definitions for yielder that I've seen before include "One who concedes" , "One who surrenders" , "producer" , "One giving way to pressure" , "One who gives way" .)