Popular drink one duke finds tasteless (7)
I believe the answer is:
insipid
'tasteless' is the definition.
('insipid' can be a synonym of 'tasteless')
'popular drink one duke' is the wordplay.
'popular' becomes 'in'.
'drink' becomes 'sip' (I've seen this before**).
'one' becomes 'i' (Roman numeral).
'duke' becomes 'd'.
'in'+'sip'+'i'+'d'='INSIPID'
'finds' acts as a link.
(Other definitions for insipid that I've seen before include "flat" , "Lacking taste or flavour" , "Boring and lacking liveliness" , "Very weak" , "dry" .)