Quick to grow old in outer Ecuador (5)
I believe the answer is:
eager
'quick' is the definition.
(thesaurus)
'grow old in outer ecuador' is the wordplay.
'grow old' becomes 'age' (synonyms).
'in' means one lot of letters goes inside another.
'outer' means to remove the middle letters.
'ecuador' with its centre taken out is 'er'.
'age' going within 'er' is 'EAGER'.
'to' is the link.
(Other definitions for eager that I've seen before include "Keen (as a beaver?)" , "really keen" , "Alert and active type?" , "Keenly interested" , "Enthusiastic, full of desire" .)