This chap's in bright cap (5)
I believe the answer is:
limit
'cap' is the definition.
(I know that cap is a more specific form of the action limit)
'this chap's in bright' is the wordplay.
'this chap' becomes 'im' (I can't justify this - if you can you should believe this answer much more).
'in' is an insertion indicator.
'bright' becomes 'lit' (similar in meaning).
'im' going within 'lit' is 'LIMIT'.
Can you help me to learn more?
(Other definitions for limit that I've seen before include "verge" , "Put restriction on" , "Restrict to a specified amount" , "Confine to specific boundary" , "Constrain" .)