That female egghead's arrived! (4)
I believe the answer is:
here
'arrived' is the definition.
The answer and definition are not the same part of speech. However, past participle verbs and adjectives sometimes mean the same thing.
'that female egghead's' is the wordplay.
'that female' becomes 'her' ('her' refers to a woman).
'egghead' becomes 'e' (head letter of 'egg').
'her'+'e'='HERE'
Can you help me to learn more?
(Other definitions for here that I've seen before include "At this stage" , "The present location" , "In this place - present" , "In attendance" , ""___ be dragons" (old map inscription?)" .)