Illegally seize something inherited during sleep (6)
I believe the answer is:
kidnap
'illegally seize' is the definition.
(kidnapping someone is seizing them illegally)
'something inherited during sleep' is the wordplay.
'something inherited' becomes 'DNA' (DNA comes from one's parents).
'during' indicates putting letters inside.
'sleep' becomes 'kip' (synonyms).
'dna' inserted into 'kip' is 'KIDNAP'.
(Other definitions for kidnap that I've seen before include "Seize, usually for ransom" , "Take person prisoner for ransom" , "Take as hostage" , "'Abduct, snatch (6)'" , "Seize and hold for ransom" .)