Here, as at Bognor, a little chap lives (5)
I believe the answer is:
regis
'here as at bognor a little' is the definition.
I don't know anything about this answer so I cannot judge whether this works.
'chap lives' is the wordplay.
'chap' becomes 'reg' ().
'lives' becomes 'is' ('be' can be a synonym of 'live').
'reg'+'is'='REGIS'
Can you help me to learn more?
(Other definitions for regis that I've seen before include "See 9" , "See 1" , "Bognor or Lyme" , "See 19" , "Kingly honorific" .)