Surprisingly, my ant aspiring to be large insect (7,6)
I believe the answer is:
praying mantis
'be large insect' is the definition.
'surprisingly my ant aspiring' is the wordplay.
'surprisingly' is an anagram indicator (a surprising ordering of the letters).
'my'+'ant'+'aspiring'='myantaspiring'
'myantaspiring' anagrammed gives 'PRAYING MANTIS'.
'to' acts as a link.
(Other definitions for praying mantis that I've seen before include "Predatory insect" , "Small creature" , "Carnivorous insect resembling a grasshopper" , "Pagan ministry (anag.)" , "Large carnivorous insect" .)