Ideology of holy Popish structure (10)
I believe the answer is:
philosophy
'ideology' is the definition.
(thesaurus)
'holy popish structure' is the wordplay.
'structure' is an anagram indicator.
'holy'+'popish'='holypopish'
'holypopish' is an anagram of 'PHILOSOPHY'.
'of' is the link.
(Other definitions for philosophy that I've seen before include "Study of truth - attitude to life" , "Eg, Stoicism" , "School of thought" , "Pursuit of truth and understanding" , "Study of the nature of knowledge and reality" .)