Stripy designs covering navy fabrics (6)
I believe the answer is:
linens
'fabrics' is the definition.
(linen is a kind of fabric)
'stripy designs covering navy' is the wordplay.
'stripy designs' becomes 'lines' (lines are stripes).
'covering' indicates putting letters inside.
'navy' becomes 'N' (common abbreviation eg in RN Royal Navy).
'lines' going around 'n' is 'LINENS'.
(Other definitions for linens that I've seen before include "They're made from flax" , "Fabrics made from flax plants" .)