Declines books in rest centre (4)
I believe the answer is:
ebbs
'declines' is the definition.
(ebb is a kind of decline)
'books in rest centre' is the wordplay.
'books' becomes 'bb' (two abbreviations for book).
'in' means one lot of letters goes inside another.
'centre' means to look at the middle letters.
The middle of 'rest' is 'es'.
'bb' going inside 'es' is 'EBBS'.
(Other definitions for ebbs that I've seen before include "Declines gradually" , "Subsides" , "Flows back or recedes" , "fades away" , "Goes out like tide" .)