Exclude some bits at centre (4)
I believe the answer is:
omit
'exclude' is the definition.
(I know that exclude can be written as omit)
'some bits at centre' is the wordplay.
'some' becomes 'om' (I am not sure about this - if you are sure you should believe this answer much more).
'at centre' means to look at the middle letters.
The centre of 'bits' is 'it'.
'om'+'it'='OMIT'
(Other definitions for omit that I've seen before include "Leave out, perhaps in error" , "Leave out or forget" , "Take out" , "Fail to mention" , "Fail (to do something)" .)