Bill staggered Cyril, showing fibre (7)
I believe the answer is:
Here is my best explanation:
'fibre' is the definition.
(acrylic is a kind of fibre)
'bill staggered cyril' is the wordplay.
'bill' becomes 'ac'.
'staggered' indicates an anagram.
'cyril' is an anagram of 'rylic'.
'showing' is the link.
(Other definitions for acrylic that I've seen before include "Type of hard paint", "Fibre", "Textile fibre - icy Carl (anag)", "Synthetic resin or fibre used for textiles", "Type of twenty Dn", "Kind of paint", "Synthetic fabric", "fibre that's synthetic", "Pungent acid" and "material for coat?".)