Thick-skinned type, my padre, crazy about church (9)
I believe the answer is:
pachyderm
'thick-skinned type' is the definition.
'my padre crazy about church' is the wordplay.
'crazy' indicates anagramming the letters.
'about' means one lot of letters goes inside another.
'church' becomes 'ch' (common abbreviation).
'my'+'padre'='mypadre'
'mypadre' anagrammed gives 'payderm'.
'payderm' placed around 'ch' is 'PACHYDERM'.
(Other definitions for pachyderm that I've seen before include "jumbo" , "Animal with very thick skin, elephant say" , "Large mammal" , "Insensitive sort" , "Rhino or hippo, say?" .)