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' means one lot of letters go next to another.
'essayist' becomes 'elia' (pseudonym of Charles Lamb).
'lob'+'elia'='LOBELIA'
'that's' is the 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" .)