Tiny brain? Reptile with it going after half of mine! (9)
I believe the answer is:
microchip
'tiny brain?' is the definition.
'reptile with it going after half of mine' is the wordplay.
'reptile' becomes 'croc' (I've seen this before).
'with it' becomes 'hip' (I've seen this in other clues**).
'going after' means one lot of letters go next to another.
'half of' means to take half the letters.
'mine' halved is 'mi'.
'croc'+'hip'='crochip'
'crochip' after 'mi' is 'MICROCHIP'.
(Other definitions for microchip that I've seen before include "Silicon implant" , "Tiny proportion of potato" , "Bit of hardware" , "Integrated circuit" , "little conductor" .)