Shrub extremely likely to be quite old (7)
I believe the answer is:
elderly
'be quite old' is the definition.
(I've seen this before)
'shrub extremely likely' is the wordplay.
'shrub' becomes 'elder' (elder is a kind of shrub).
'extremely' suggests removing the centre (only the extremes of the word are used).
'likely' with its centre removed is 'ly'.
'elder'+'ly'='ELDERLY'
'to' acts as a link.
(Other definitions for elderly that I've seen before include "Aged" , "Of advanced years" , "Mature" , "Past middle age, a senior citizen" , "Somewhat old" .)