Judge to be half dead like silly me! (4)
I believe the answer is:
deem
'judge' is the definition.
(I've seen this before)
'half dead like silly me' is the wordplay.
'half' means to take half the letters.
'like silly me' becomes 'em' (I can't justify this - if you can you should believe this answer much more).
'dead' with half the letters taken is 'de'.
'de'+'em'='DEEM'
'to be' acts as a link.
Can you help me to learn more?
(Other definitions for deem that I've seen before include "Regard, consider" , "Adjudge" , "Believe" , "Judge in redeeming" , "Card-table felt" .)