Watchful, having British chain (6)
I believe the answer is:
albert
'chain' is the definition.
(I've seen this before)
'watchful having british' is the wordplay.
'watchful' becomes 'alert ' (similar in meaning).
'having' indicates putting letters inside.
'british' becomes 'b' (abbreviation e.g. in BBC).
'alert' going around 'b' is 'ALBERT'.
(Other definitions for albert that I've seen before include "- - Finney" , "Victim of lion" , "M [MUSEUM] with 18 [VICTORIA]" , "Kind of watch chain" , "watch may depend on it" .)