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' means one lot of letters go next to another.
'time' becomes 't' (abbreviation).
'ma'+'t'='MAT'
'for' is the 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" .)