Old wood put on walls of library (7)
I believe the answer is:
elderly
'old' is the definition.
(I know that old can be written as elderly)
'wood put on walls of library' is the wordplay.
'wood' becomes 'elder' (type of tree).
'put on' is a charade indicator (letters next to each other).
'walls of' says to hollow out the word (remove centre letters) (only the edge letters remain).
'library' with its centre removed is 'ly'.
'elder'+'ly'='ELDERLY'
(Other definitions for elderly that I've seen before include "Long in the tooth" , "Past middle age, a senior citizen" , "Fairly old, past middle age" , "Old or ageing" , "Rather old" .)