Tree extremely likely to be quite old (7)
I believe the answer is:
elderly
'be quite old' is the definition.
(I've seen this before)
'tree extremely likely' is the wordplay.
'tree' becomes 'elder' (elder is a kind of tree).
'extremely' suggests removing the centre (only the extremes of the word are used).
'likely' with its middle removed is 'ly'.
'elder'+'ly'='ELDERLY'
'to' acts as a link.
(Other definitions for elderly that I've seen before include "Long in the tooth" , "Not young" , "Mature" , "over the hill" , "Somewhat old" .)