My first drink supplier leaves on time (4)
I believe the answer is:
teat
'my first drink supplier' is the definition.
(a teat supplies milk to a baby)
'leaves on time' is the wordplay.
'leaves' becomes 'tea' (as in tea leaves).
'on' means one lot of letters go next to another.
'time' becomes 't' (abbreviation).
'tea'+'t'='TEAT'
(Other definitions for teat that I've seen before include "Bulb on infant's bottle" , "essential for babies" , "Part of feeding bottle" , "Piece on baby's bottle" , "Nipple or dug" .)