Part of foot to squeeze, but not softly! (4)
I believe the answer is:
inch
'part of foot' is the definition.
(12 inches in a foot)
'squeeze but not softly' is the wordplay.
'squeeze' becomes 'pinch' (synonyms).
'but not' suggests deleting specific letters.
'softly' becomes 'p' (short for piano, musical term for softly).
'pinch' with 'p' taken away is 'INCH'.
'to' acts as a link.
(Other definitions for inch that I've seen before include "Fraction of a foot" , "1/12 of foot" , "Move slowly and cautiously" , "One point 63380 th of a mile" , "0.08333 of a foot" .)