Some medicine making us drowsier, oddly (4)
I believe the answer is:
dose
'some medicine' is the definition.
(dose is a kind of medicine)
'drowsier oddly' is the wordplay.
'oddly' means one should take alternating letters (letters in the odd-numbered positions are used).
The alternating letters of 'drowsier' are 'DOSE'.
'making us' acts as a link.
(Other definitions for dose that I've seen before include "Helping of medicine" , "Give drugs to (a person)" , "Measure of medicine" , "Medicinal quantity" , "Measure (med.)" .)