Mother has time for rug (3)
I believe the answer is:
mat
'rug' is the definition.
(both are floor coverings)
'mother has time' is the wordplay.
'mother' becomes 'ma' (ma can mean mother).
'has' says to put letters next to each other.
'time' becomes 't' (abbreviation).
'ma'+'t'='MAT'
'for' acts as a link.
(Other definitions for mat that I've seen before include "dull finish" , "A piece of material as floor covering" , "To wipe your feet on" , "Small carpet" , "Paint with a dull surface" .)