Mature and wise? Not initially (3)
I believe the answer is:
age
'mature' is the definition.
('age' can be a synonym of 'mature')
'wise? not initially' is the wordplay.
'wise?' becomes 'sage' ('sage' can be similar in meaning to 'wise').
'not initially' means to remove the first letter.
'sage' with its first letter removed is 'AGE'.
'and' is the link.
(Other definitions for age that I've seen before include "Get older" , "Historical period" , "Long period" , "Grow older" , "16/18 [INDUSTRIAL REVOLUTION]" .)