Very extrovert principal wearing fancy shirt with flourishes (7)
I believe the answer is:
thrives
'flourishes' is the definition.
(I know this)
'very extrovert principal wearing fancy shirt' is the wordplay.
'principal' suggests taking the first letters.
'wearing' indicates putting letters inside.
'fancy' indicates anagramming the letters.
The first letters of 'very extrovert' is 've'.
'shirt' with letters rearranged gives 'thris'.
've' inserted into 'thris' is 'THRIVES'.
'with' is the link.
(Other definitions for thrives that I've seen before include "Develops well" , "Is very healthy and does well" , "Flourishes, prospers" , "Prospers, does well" .)