Books with their own shelf at the Royal Society (7)
I believe the answer is:
ledgers
'books' is the definition.
('ledger' can be a synonym of 'book')
'shelf at the royal society' is the wordplay.
'shelf' becomes 'ledge' (synonyms).
'at' means one lot of letters go next to another.
'the royal society' becomes 'rs'.
'ledge'+'rs'='LEDGERS'
'with their own' acts as a link.
I am not very happy about this link. Some or all of it may belong to another bit of the clue.
Can you help me to learn more?
(Other definitions for ledgers that I've seen before include "Account books" , "old spreadsheets" , "Books listing commercial transactions" , "Books of accounts" , "Account-books" .)