Graduate has time for rug (3)
I believe the answer is:
mat
'rug' is the definition.
(I've seen this before)
'graduate has time' is the wordplay.
'graduate' becomes 'ma' (abbreviation for Master of Arts).
'has' means one lot of letters go next to another.
'time' becomes 't'.
'ma'+'t'='MAT'
'for' acts as a link.
(Other definitions for mat that I've seen before include "knot" , "dull finish" , "Dull, rug" , "Unglossy floor pad" , "Small carpet" .)