Priest holding firm is a cause of complaints (1,4)
I believe the answer is:
e coli
'cause of complaints' is the definition.
'e coli' can be an answer for 'cause' (I have seen 'Cause of infection' mean 'e coli' so perhaps 'cause' could also mean 'e coli'). I am not sure about the 'of complaints' bit.
'priest holding firm' is the wordplay.
'priest' becomes 'eli' (biblical figure).
'holding' means one lot of letters goes inside another.
'firm' becomes 'co' (a firm is a company).
'eli' placed around 'co' is 'E COLI'.
'is a' is the link.
Can you help me to learn more?
(Other definitions for e coli that I've seen before include "Bacterium found in the gut" , "Cause of infection" , "Common species of bacterium" , "Type of bacteria causing food poisoning" , "Some types of this bacterium are toxic" .)