Game roughly drawn up at hospital (7)
I believe the answer is:
canasta
'game' is the definition.
(canasta is a kind of game)
'roughly drawn up at hospital' is the wordplay.
'roughly' becomes 'ca' (abbreviation for circa).
'drawn up' says the letters should be written in reverse.
'hospital' becomes 'san' (short for sanatorium).
'at'+'san'='atsan'
'atsan' backwards is 'nasta'.
'ca'+'nasta'='CANASTA'
(Other definitions for canasta that I've seen before include "Two-pack card game" , "this needs two packs" , "Card game of the rummy family" , "Can a staff cook stomach game?" , "Card game resembling rummy" .)