Minute part in codes Einstein finally cracked (6)
I believe the answer is:
second
'minute part' is the definition.
('second' is part of 'minute')
'codes einstein finally cracked' is the wordplay.
'finally' suggests the final letters.
'cracked' indicates anagramming the letters.
The last letter of 'einstein' is 'n'.
'codes'+'n'='codesn'
'codesn' anagrammed gives 'SECOND'.
'in' is the link.
(Other definitions for second that I've seen before include "Endorse, back" , "Back-up; short time" , "additional > support" , "Back (but not first!)" , "Lower < back" .)