Famous Conservative delighted to ring oddly absent member (10)
I believe the answer is:
celebrated
'famous' is the definition.
(I know that famous can be written as celebrated)
'conservative delighted to ring oddly absent member' is the wordplay.
'conservative' becomes 'C' (UK political abbreviation).
'delighted' becomes 'elated' (I've seen this before).
'to ring' means one lot of letters goes inside another.
'oddly absent' indicates alternate letters (odd-numbered letters removed).
The alternate letters of 'member' are 'ebr'.
'elated' going around 'ebr' is 'elebrated'.
'c'+'elebrated'='CELEBRATED'
(Other definitions for celebrated that I've seen before include "Did something enjoyable (to mark an event)" , "Observed (festival); famous" , "Cheered" , "Rejoiced - famous" , "Eminent" .)