Period of aspiration suffering setback, Conservative admitted (5)
I believe the answer is:
epoch
'period' is the definition.
(epoch is a kind of period)
'aspiration suffering setback conservative admitted' is the wordplay.
'aspiration' becomes 'hope' (I've seen this before).
'suffering setback' says the letters should be written backwards.
'conservative' becomes 'c' (abbreviation commonly used in UK politics).
'admitted' indicates putting letters inside.
'hope' written backwards gives 'epoh'.
'epoh' enclosing 'c' is 'EPOCH'.
'of' acts as a link.
(Other definitions for epoch that I've seen before include "Significant period" , "Geological time period" , "Period of time in history" , "Distinctive period of time" , "Unit of geological time" .)