That's the English for you! (4)
I believe the answer is:
thee
'you' is the definition.
(I've seen this before)
'that's the english' is the wordplay.
'that's the' becomes 'the'.
'english' becomes 'E' (abbreviation).
'the'+'e'='THEE'
'for' acts as a link.
(Other definitions for thee that I've seen before include "Poetically you" , "Quaker 'you'" , "you many years ago" , "You (arch.)" , "'U'" .)