Person initially unwell needs medicine (4)
I believe the answer is:
pill
'medicine' is the definition.
(pill is a kind of medicine)
'person initially unwell' is the wordplay.
'initially' says to take the initial letters.
'unwell' becomes 'i'll' (similar in meaning).
The first letter of 'person' is 'p'.
'p'+'ill'='PILL'
'needs' acts as a link.
(Other definitions for pill that I've seen before include "Form of medicine" , "Pellet of medicine" , "Medication" , "Medical tablet" , "Dreadful person" .)