Irregular, but attending church in case of publicity (6)
I believe the answer is:
patchy
'irregular' is the definition.
(thesaurus)
'attending church in case of publicity' is the wordplay.
'attending' becomes 'at' (I've seen this in other clues**).
'church' becomes 'ch' (common abbreviation).
'in' means one lot of letters goes inside another.
'case of' suggests removing the centre (outsides of).
'publicity' with its centre removed is 'py'.
'at'+'ch'='atch'
'atch' inserted within 'py' is 'PATCHY'.
'but' acts as a link.
(Other definitions for patchy that I've seen before include "Irregular or uneven" , "Irregular in quality" , "Sporadic, irregular" , "Inconsistent" , "Uneven in quality - mended too often" .)