Regular church people first to trace old paper (9)
I believe the answer is:
parchment
'old paper' is the definition.
'regular church people first to trace' is the wordplay.
'regular' becomes 'par' (both can mean standard or typical).
'church' becomes 'ch' (common abbreviation).
'people' becomes 'men' (men can refer to humanity as a whole).
'first to' says to take the initial letters.
The first letter of 'trace' is 't'.
'par'+'ch'+'men'+'t'='PARCHMENT'
(Other definitions for parchment that I've seen before include "Old writing material" , "quality paper" , "Paper made from animal skin" , "sheepskin" , "diploma" .)