They're waspish in a big way (7)
I believe the answer is:
hornets
'they're waspish' is the definition.
The definition suggests an adverb but the answer is not.
'big way' is the wordplay.
I cannot really see how this works, but
'way' could be 's' (Compass direction - South) and 's' is found in the answer.
The remaining letters 'hornet' is a valid word which might be clued in a way I don't see.
This explanation may well be incorrect...
'in a' is the link.
Can you help me to learn more?
(Other definitions for hornets that I've seen before include "Large type of wasps" , "Large stinging wasps" .)