Russell conceals life's little ironies primarily from party in coalition (8)
I believe the answer is:
alliance
'coalition' is the definition.
(I know that coalition can be written as alliance)
I cannot understand how the remainder of the clue works.
Can you help me to learn more?
(Other definitions for alliance that I've seen before include "Association for mutual benefit" , "Federation" , "Union, association" , "Kind of partnership with canaille" , "Confederation" .)