Hospital patient's heart to pound; one in bed, perhaps is not so flat (7)

'not so flat' is the definition.
(hilly is the opposite of flat)

'hospital patient's heart to pound one in bed perhaps' is the wordplay.
'hospital' becomes 'h'.
'patient's' becomes 'vaccinees' (vaccinee is a kind of patient).
'heart' means to look at the middle letters.
'to pound' becomes 'l'.
'one in bed perhaps' becomes 'lier' (somebody lying down).
The central letter of 'vaccinees' is 'i'.
'h'+'i'+'l'+'lier'='HILLIER'

'is' acts as a link.