Time in greeting Roman Catholic this Roman ranked (10)
I believe the answer is:
hierarchic
'ranked' is the definition.
(similar in meaning)
'time in greeting roman catholic this roman' is the wordplay.
I cannot quite see how this works, but
'time' could be 'era' (an era is a period of time) and 'era' is present in the answer.
'in' could be 'chic' (in can mean chic or fashionable) and 'chic' is located in the answer.
'greeting' could be 'hi' (hi is a kind of greeting) and 'hi' is found within the answer.
A single letter 'r' remains which might be clued in a way I don't see.
This may be the basis of the clue (or it may be nonsense).
Can you help me to learn more?
(Another definition for hierarchic that I've seen is " Arranged in order of rank".)