Eagle on top of tree bursting to stretch out (8)
I believe the answer is:
elongate
'stretch out' is the definition.
(thesaurus)
'eagle on top of tree bursting' is the wordplay.
'top of' indicates taking the first letters.
'bursting' indicates anagramming the letters.
The first letter of 'tree' is 't'.
'eagle'+'on'+'t'='eagleont'
'eagleont' anagrammed gives 'ELONGATE'.
'to' is the link.
(Other definitions for elongate that I've seen before include "Open out" , "Stretch, pull" , "appearing to be slender" , "Make longer" , "Stretch, lengthen" .)