Perch in centre to eat away (7)
I believe the answer is:
corrode
'eat away' is the definition.
(I've seen this before)
'perch in centre' is the wordplay.
'perch' becomes 'rod' (synonyms).
'in' indicates putting letters inside.
'centre' becomes 'core' (core can mean something's centre).
'rod' going within 'core' is 'CORRODE'.
'to' is the link.
(Other definitions for corrode that I've seen before include "Eat away, rust" , "Eg, to rust" , "Destroy metal gradually by chemical action" , "Gradually weaken (by chemical action)" , "Growth in hazel buds" .)