Picks length to cut new carpet (7)
I believe the answer is:
plectra
'picks' is the definition.
('plectron' can be a synonym of 'pick')
'length to cut new carpet' is the wordplay.
'length' becomes 'l' (abbreviation in geometry).
'to cut' means one lot of letters goes inside another (some letters cut their way into a word).
'new' indicates an anagram.
'carpet' with letters rearranged gives 'pectra'.
'l' inserted within 'pectra' is 'PLECTRA'.
(Other definitions for plectra that I've seen before include "Parts for harpsichord" , "Guitar picks" , "Plucky types" , "Bits of plastic maybe" , "Guitar pickers - carp let (anag)" .)