Turns up, agency starts spreading old mistakes - therein lies the pattern (6)
I believe the answer is:
mosaic
'the pattern' is the definition.
(mosaic is a kind of pattern)
'turns up agency starts spreading old mistakes' is the wordplay.
'turns up' says the letters should be written in reverse.
'agency' becomes 'cia' (CIA is an example**).
'starts' says to take the initial letters.
The first letters of 'spreading old mistakes' is 'som'.
'cia'+'som'='ciasom'
'ciasom' in reverse letter order is 'MOSAIC'.
'therein lies' acts as a link.
I am not very happy about this link. Some or all of it may belong to another bit of the clue.
Can you help me to learn more?
(Other definitions for mosaic that I've seen before include "Design made of small pieces of colored stone or glass" , "Tessellated pattern" , "Design of little pieces" , "It is pieced together" , "Small pieces fitted together" .)