Flower that's shot up seen by essayist (7)
I believe the answer is:
lobelia
'flower' is the definition.
(I've seen this before)
'shot up seen by essayist' is the wordplay.
'shot up' becomes 'lob' (I've seen this before).
'seen by' is a charade indicator (letters next to each other).
'essayist' becomes 'elia' (pseudonym of Charles Lamb).
'lob'+'elia'='LOBELIA'
'that's' acts as a link.
(Other definitions for lobelia that I've seen before include "Oil bale (anag) - flower" , "Garden plant with five-lobed flowers" , "something flowery" , "Lo, I bale out the flower" , "Flower used for hanging baskets" .)