Having second thoughts, make change to prayer book (7)
I believe the answer is:
psalter
'to prayer book' is the definition.
(Psalter is an example)
'having second thoughts make change' is the wordplay.
I cannot quite see how this works, but
'second' could be 's' (common abbreviation) and 's' is found within the answer.
'change' could be 'alter' (synonyms) and 'alter' is located in the answer.
A single letter 'p' remains which might be clued in a way I don't understand.
This explanation may well be incorrect...
Can you help me to learn more?
(Other definitions for psalter that I've seen before include "sacred work" , "Church chanting book" , "Cherub-like" , "Books of Psalms" , "Book for church use" .)