Bring out priest before start of church appeal (6)
I believe the answer is:
elicit
'bring out' is the definition.
(thesaurus)
'priest before start of church appeal' is the wordplay.
'priest' becomes 'eli' (I've seen this before**).
'before' means one lot of letters go next to another.
'start of' indicates taking the first letters.
'appeal' becomes 'it'.
The first letter of 'church' is 'c'.
'eli'+'c'+'it'='ELICIT'
(Other definitions for elicit that I've seen before include "Bring out - evoke" , "Take or draw from" , "Call forth, educe" , "'Draw out, evoke (6)'" , "Draw out (response, information etc)" .)