That is a sign of penitence, in a way (8)
I believe the answer is:
scilicet
'that is' is the definition.
(I've seen this before)
'a sign of penitence in a way' is the wordplay.
'a sign of penitence' becomes 'cilice' (I can't explain this - if you can you should believe this answer much more).
'in' is an insertion indicator.
'a way' becomes 'st' (abbreviation for street).
'cilice' going into 'st' is 'SCILICET'.
Can you help me to learn more?
(Other definitions for scilicet that I've seen before include "That is to say" , "Introduction to explanation" , "Namely" .)