Blanket unravels badly, one's admitted (9)
I believe the answer is:
universal
'blanket' is the definition.
(I've seen this before)
'unravels badly one's admitted' is the wordplay.
'badly' is an anagram indicator (letters in the wrong order).
'one' becomes 'i' (Roman numeral).
'admitted' indicates putting letters inside (inserted letters are admitted in).
'unravels' with letters rearranged gives 'unversal'.
'unversal' going around 'i' is 'UNIVERSAL'.
(Other definitions for universal that I've seen before include "Without exception" , "Everywhere applicable" , "Of worldwide scope" , "for general viewing" , "affecting everyone" .)