Lying down in suite, finally, after drink (6)
I believe the answer is:
supine
'lying down' is the definition.
(being supine is lying on one's back)
'in suite finally after drink' is the wordplay.
'finally' says to take the final letters.
'after' means one lot of letters go next to another.
'drink' becomes 'sup' (to sup is to drink).
The last letter of 'suite' is 'e'.
'in'+'e'='ine'
'ine' put after 'sup' is 'SUPINE'.
(Other definitions for supine that I've seen before include "Lying on one's back - passive" , "looking up" , "Lying face upwards, indolent" , "Slow in acting" , "Flat on one's back" .)